Nomenclature has become a virtually always very annoying and sometimes insurmountable problem among those who listen to electronic music in all of its guises. Because electronic music is such a new form, fifty years old at best, different camps around the world may be making the same noises at a given time and calling them completely different names. When somebody has become used to speaking of a certain musical style by a certain name, being convinced to call it something else is improbable. Hence, listeners from the most disaffected dilletantes to the hardest-core devotees are often each talking about slightly different things, and perpetuating the confusion.
This shouldn't be that hard. And indeed, over the last five years it has become much less so in some ways. Unfortunately, over the same time it has become even more so in others:
In one camp we have the music journalists, who call the same styles by the same names whether they're from Europe, the US, Japan, or elsewhere. They have standardized for their (and our) own good, and are slowly dragging their reading, watching, and listening audiences out of the mire. Note that this applies to journalists who are really interested in the music, rather than MTV marketing executives and other sundry parasites.
In the other camp is popular culture, which got ahold of electronic music well before this consolidation in Europe, and even slightly beforehand everywhere else. Because bookstores (notably the Hastings chain; others too), MTV, and the fourteen-year-olds wearing phat pants at the mall refer to Moby as "techno", that categorization and the laziness it represents continues among people who are completely new to the music. For an example of this sort of poisonous stupidity, see the node Types of techno, which is more-or-less completely incorrect.
So, what should one call the music, if they don't know the "proper" name? Electronic music. It's that simple, and that's why this writeup is under that node. Calling something electronic music is the lowest and safest common denominator in, well, electronic music. If you can tell positively that it's dance oriented, go ahead and call it "electronic dance music", and I wish you luck choking out that mouthful in conversation. Otherwise, simply "electronic music" will suffice.
Roughly speaking, electronic music breaks down into two categories, though (surprise!) there is enough overlap between them to make the decision difficult. Dance oriented electronic music is created explicitly for people to dance to, and its other listening avenues are often not an issue. Because electronic dance music is made for moving one's body to, its rhythm generally falls in a certain range of beats per minute (BPM) for a given genre. Electronic music meant for listening to in other contexts may lack the persistent beat and other stereotypical hallmarks of dance music, making it much easier for many to appreciate.
Note that this writeup is not a metanode, nor does it pretend to be comprehensive! Rather, it is an explicated list of the standardized names of those forms which have been stable long enough to have the word "established" attributed to them. When the words below are used by a reliable source or well media-informed listener, one can be sure they mean what this writeup says they do.
Hip-Hop: The grand-daddy of dance oriented electronic music, Hip-Hop has existed in one form or another for more than twenty-five years. It is characterized by a rhythm line of a single 4/4 breakbeat measure, repeated with or without variation and musical samples at between 100 and 130 BPM. See ZamZ's writeup under Hip Hop regarding the culture, though there don't seem to be any writeups about the musical structure itself.
House: This style also goes way back, and has its roots in the steady pulse of late 70's disco. It has a four on the floor bass drum beat, and often simple, non-polyrhythmic accompaniment in the rhythm line; it stays around 110 to 135 BPM, though modified forms may go much faster. House music often has an actual melody to it, something one could hum, as opposed to some of the more abstract electronic forms. See j-dog's writeup under House about the music, but take its info on House music culture with a few grains of salt.
Drum & Bass / Jungle: Nomenclature is difficult with this one, and depending on who you ask still undecided; whether the two are identical or different, the basic rhythm and speed is the same in both, and that's what we're going off of here. This form is based on breakbeat rhythms, usually combined with a powerful bassline that may dip all the way into sub-sonic ranges. It is much, much faster than most, varying between 160 and 240 or more (!) BPM. See Great Neb's excellent writeup under Drum & Bass.
Techno: Techno was, starting fifteen or twenty years ago, a regional offshoot of house local to Detroit. With time, its formula has deviated so significantly from standard house that even mixing the two together would today be almost impossible. Techno keeps house's 4/4 bass drum line, but adds layers and layers of other shifting, polyrhythmic instruments, bringing its rhythmic complexity up to the level of IDM (see below). It may or may not -- usually not these days -- have any melody to speak of, and runs at between 130 and 160 BPM. See mkb's flawless writeup under Techno for everything more you want to know.
Trance: Another branch of house, and one of the most recent on this list to establish itself independently. This simplifies the house beat usually to just one or two instruments besides the steady bass drum, and often adds long, intense melodies. It shares some heritage with ambient, and may have long stretches where the melody continues without any dance rhythm at all. Recently (for two or three years) there has been a trend of using breakbeats in Trance tunes. People tend to get Ambient confused with Trance because they may both be appropriate for "spiritual" listening; however, if a tune doesn't have a bass drum somewhere, it's not Trance. Trance goes between 130 and 150 BPM. See StrawberryFrog's writeup under Trance music for a little more.
Breaks: Think the rhythm of Hip-Hop with the soul, melody, and tempo of house. Actually, Breaks have been described as "house with some of the beats missing", which isn't really correct but points out the similarity between the two genres; some DJs even mix the two together in their set. Also like House, Breaks generally come between 110 and 135 BPM, with more variation in some of their new forms.
Dub: Originally (in the very late 60's) instrumental Reggae music passed through delays and other effects processors to change it completely, now a genre unto itself which also combines elements of House and Ambient. S-l-o-w moving dance music, generally between 70 and 120 BPM. Dub is really more like a proto-form of electronic music, given its reliance on non-electronic instruments for most or all of its sounds, at least in its original form. See Protector of Mankind's writeup under Dub for a solid, concise history of the form.
IDM: Which stands for Intelligent Dance Music -- again, nomenclature would seem to put it as a form of, well, dance music, but upon listening to some one learns quickly that it isn't. As with the rest of the unstructured, non-dance electronic forms, this genre is difficult to generalize about. It will virtually always have percussion instruments of some kind, which differentiates it from Ambient, and will more often than not have a rhythm line made up of breakbeats, often modified to unrecognizability. See Lost and Found's writeup under IDM.
Ambient: Ambient music works by creating soundscapes, musical collages of sound in motion rather than patterns of notes. Unlike all forms listed thus far, it generally features no percussion at all, or percussion instruments used just for the way they sound. In more extreme forms, no tempo is kept, leaving the sound positioning solely at the artist's discretion. Echoes, reverbs, and other forms of studio processing are common. See res0nat0r's writeup in Ambient for a short list of artists.
Electronica: Shares some features of dance music and IDM, and IDM is even called electronica by some informed listeners. Electronica is sort of a catch-all genre for easy listening electronic music, which (unlike the other forms) often features a vocalist. It probably has a "danceable" beat, but is not intended for the dance floor. Some indie rock bands tend toward Electronica's territory, and indeed Electronica is the closest of any form of electronic music to good old rock and roll. Make no mistake, by the way, the word "electronica" is not to be used in place of "electronic music" -- it is a subset like any of the others. Unable to find a good Electronica writeup to reference here.
Classical: Electronic music artists who do not intend their pieces for any mainstream audience, but instead for the staid, academic Classical music crowd, may thus be considered to be composing Classical music. Generalization is hardest of all here, as almost by definition these pieces are wholly unlike the music that exists before them. More pretentious Electronica and IDM producers will sometimes try to pass their work off as Classical, but unless they attribute their given name to it at the very least, they are just posing. At risk of posting metanode material, Steve Reich and Paul Lansky are two more-famous composers of electronic Classical music.
If you are about to message me that your favorite style is missing from the list, first re-read the paragraph about a style of electronic music being well and truly established before its inclusion here. Then, if I've missed out on something which has been around for five or ten years, go ahead and tell me.