Friendships exist in many forms.
I will attempt to classify them here according to the experiences I have gained through my, until now, relatively short life. As suggested by a fellow noder, I will also try to accompany each "class" with some appropriate examples.
This kind of friendship is probably the most frequent in existence all throughout your life. At several times will you meet someone new, strike up a conversation of sorts only to realize that you have very little in common. Obviously this can hardly be classified as a friendship. However, this type of encounter is at least metaphorically close to meeting someone, inviting them over, and then deciding that never seeing them again would be too soon. Again, this is a harsh exaggeration and rarely have I myself experienced this kind of friendship. Whether you are on the receiving or dispensing end of the brush off, is relatively irrelevant.
Fact is that hardly any kind of emotional bond arises from such a short encounter, and if it does, then it is likely based on a pre-existing infatuation from one of the involved parties. As such, being the person who is brushed off is of course not a comfortable thing, but not soul-crushing either.
Example: Coming up with examples in this particular category can be tricky, because in my opinion, temporary friendships are rarely memorable. And if they are then often I wish to forget them because I was the one who found myself uncomfortable within it. I do however remember one particlar person in school which I had a very rough time of avoiding. To set things straight, I never actively avoided the person or hid from him, but if I were to spot him before he spotted me I often contemplated the reason for me being wherever I was and if there was still a reason to be there. He was all-in-all a friendly guy, but he simply couldn't talk about anything except this one game. I'm probably also to blame for not trying hard enough to steer the conversation a certain way or not having the heart to tell him that he was becomming annoying with this particular topic. I wonder whatever happened to him...
This is almost my personal favorite as I've been exposed to this friendship to quite a degree. It's the kind of friendship where one of the participants is unaware or in denial concerning the actual degree of friendship involved. This kind of friendship often evolves from surroundings where both parties often meet due to some circumstance unrelated to the friendship. A good example is either some kind of academic surrounding (school or university for example), work or even physical activity (soccer practice etc.).
As opposed to the previous described friendship, being of either side of the friendship is very relevant. One party is involved as far as talking, sharing and otherwise interacting with the other party without any real intention of furthering the friendship (let's call this party B). The other party is equally involved but with an interest in furthering it (party A). This is the deciding factor between being on either end of the friendship.
A tell tale sign of this is one of the parties involved arranging social engagements where the other is not invited or even informed. The scariest thing about this kind of friendship is that it can evolve so far that party A becomes very aware of social gatherings - even discussed right in front of their nose - and still not being invited.
Of course, the more this continues the less awkward it becomes for party B. But of course, by this time party A is well enough into denial about the state of the friendship that party A probably doesn't even care.
The point is that party B doesn't dislike party A as they can get along well, but there is no interest at all to continue the pleasantries outside the circumstance they normally meet in. Personally I detest being in this kind of friendship even though I am fully aware of it. Not because Party B is malicious in any way. I personally know lot's of people I like but have no further interest in.
I suppose it concerns the feeling of being fooled and no doubt my personal experience relating to this kind of friendship.
Example: Practically every "friend" I had in a two year period in school falls under this category. People I thought I got along great with and enjoyed talking to. But no - whenever anything outside school was organized which wasn't organized by the school I was "oddly" enough never invited. I partially blame myself for not prodding enough which might have helped. Anyway - I still often see these people at reunions, and still enjoy talking to them, but beneath the surface I always remember how things were. Nevertheless - I hold no spite against them as such stuff will bring you nowhere. The "friends" I'm talking about ranged all the way from the jock-type people, to average students and even social outcasts. I'll never forget that in my attempt to befriend and socialize a (let's say) "socially challenged" individual I only found myself "backstabbed" in his hopes of gaining a little recognition.
The key difference between this and the former friendship is that both parties exhibit at least some amount of interest in furthering the friendship. Be it just inviting the other party over or occasionally calling the other party on the phone.
Again, the extent of involvement exhibited by both parties can vary a lot, but some amount must exist in my opinion to call it a casual friendship.
Example: Now we're getting to the good stuff. A lot of my casual friendships go hand in hand with permanent ones. I am thinking of a few particular people I also met in school who I really enjoy being with yet never really open up or seem to listen to "reason" concerning various issues. This one guy I at first found to be not shy, but still not very outward. Yet - he has a lot of admirable qualities. He's friendly and kind, but he isn't great at taking care of himself and seems to refuse to listen to any advice concerning it. Nevertheless - I really like him and that's what counts.
I have no real label for this friendship so I decided to call it permanent even though that is "wrong" in my opinion. But it was either that or call it an intimate friendship which is also believe to be "wrong".
The important point to be made concerning this friendship is that it's a friendship that extends beyond casual limits. A friendship that doesn't rely on the convenience of temporary surroundings, such as living close or often seeing each other due to various circumstances. In my opinion a deeper understanding of either each other or of a specific topic is also a common theme within this kind of friendship, or perhaps an unspoken bond.
The parties involved do not necessarily need to share feelings or other intimate details for this kind of friendship to evolve but it's much more likely to happen in this kind of friendship in my opinion.
Example: One particularly springs to mind here. I first met this guy during a social gathering at a friend. He also wasn't shy but again not very outward. My brother seemed to talk more with him than me and I honestly didn't pay a great deal of attention to him. Then, a few years have passed and due to various circumstances he starts attending the same school as me. Oddly enough our friendship had a sort of rocky start with him holding a social event and again me not being invited. However, soon afterwards we grew very close, driving to school together, hanging out almost all the time and talking a lot about more themes that I can remember. We now live far apart and only speak every couple of months, but even so - I still feel like I am on exactly the same wavelength as I always was with this guy... And it makes me smile...
Each friendship can easily falter. I have a few friends abroad that I highly appreciate, but I do not converse with them on a regular basis unless I come close by or there is a special occasion. I do not feel I've become less friends with these people and I of course want to keep them as friends, but on the other hand I'd rather invest my time and effort to make new friends and keep them where I am now instead of artificially keeping distant ones alive. I guess what I'm trying to say is I doubt I can keep me and my friends from growing apart just by calling or writing to them on a regular basis. If we grow apart then that's fate and we'll either find a new common ground or rarely speak again.