In ordinary usage an heir is someone who is going to inherit
something or has done so. In law the usage is narrower. Not being a lawyer, I don't want to go into modern laws of inheritance
, so the following is just about the traditional terminology as still used in succession
to such old-fashioned things as a lordship
or a coat of arms
An heir is strictly someone who gets things through blood line. Someone who gains lands (real property) by a will is a devisee; someone who gains chattels (personal property) by a will is a legatee. If a person doesn't make a will, then there being no such legacies, all the things go to the person's heir. Those so-called incorporeal hereditaments that can't legally be bequeathed to a person of the testator's choosing, which includes arms and titles, must go to the heir: they always descend in the blood line.
Also an heir is someone who has actually inherited something because the previous holder has died. If you haven't yet got it you're not yet the heir. Various combination terms are used to describe those who look set to be the heir in the future. The heir apparent is one whose position is secure, such as an eldest son. As long as they live they can never be displaced from number one slot in the list of hopefuls. An heir presumptive is someone such as a daughter or brother or nephew who is currently next of kin, but will be pushed out of number one slot if the holder has a son of their own. In these traditional things sons are always preferred to daughters so a daughter can be displaced by the subsequent birth of a younger brother. The heir in remainder is whichever one of an heir apparent or heir presumptive exists (there can only be one).
The heir in expectancy is an informal term for someone who isn't number one on the list but who will probably, in the normal course of nature, move up into the number one slot because everyone above them in the list is elderly, insane, or in religious orders, so unlikely to produce any permanent blood line of their own even if they do inherit ahead of the heir in expectancy.
Who is on the list? This depends on how the hereditament in question was created. Peerages and baronetcies (hereditary knighthoods) are mainly created by letters patent, as are grants of arms. These must specify in precise terms the remainder or limitation, which is a formula determining which future descendants will be eligible as heirs.
There are two main methods of descent in English and Scottish law. Remainders can be to the heir male or to the heir general. If 'male' is not specified, 'heir' by itself means 'heir general', but 'male' almost always is specified. It is very rare for females to be able to inherit titles or arms in England, though a little less rare in Scotland. Heirs male are entirely in the male line: your daughter's son can't be an heir male even though he's male. With heirs general, females are taken into account and can inherit, but younger sons are called on before elder daughters.
A further limitation commonly used is 'of the body'. If someone is created a duke and the letters patent recite a remainder to the heirs male of his body, then only his descendants can be the heirs of that dukedom. If he has none left, it goes extinct. His brother cannot inherit. But this is of course only applicable to the heirs male of the body of the original grantee. If his eldest son becames duke after him but has no children, the second duke's brother can then become the duke, because he's an heir of the body of the first duke (and heir of the second duke).
Sometimes other limitations are used. Titles may have remainders saying they can go to the grantee's brother, and the heirs male of his body. They can even go to a daughter then the heirs male of her body.
Some of the oldest peerages (1300s and so on) were created not by letters patent but by writ, summoning the person to sit as a lord in Parliament. In this case there is no specific limitation, so the title descends to the heirs general. This is how we get so many Scottish noblewomen holding very ancient titles in their own right.
Entail normally applies to land: the estate goes first to X then after his death to some named Y, not to X's heirs. A few Scottish titles however do descend this way, and the heir then is called the heir in tailzie (in England, the 'heir in entail'). Tailzie is pronounced tail-yee and may be variously written as e.g. taillie also.
Since different titles and different arms have different remainders, it is possible for them to be vested in the same people for several generations, then split apart and go to different holders if a female comes into the line.
A female heir is strictly called an heir, not an heiress. Females have the odd property that several daughters jointly become heir. Usually. Some Scottish titles go direct to the eldest daughter: I'm not sure what the condition for this is. But normally if a nobleman dies leaving three daughters but no sons, and his remainder is to his heirs general, they all three become equal coheirs. They can also be called heirs portioner or parceners or coparceners. If one dies and leaves a son, the son is now the holder of her third of the coheirship. If she died leaving two daughters they'd hold a sixth each. This state continues until all their branches are extinct except one. If their father was for example a baron, the barony goes into abeyance for as long as there is more than one coheir. (Or the Sovereign can call it out of abeyance for the eldest daughter or her sole heir.) If instead of conveniently going extinct, the multiple coheir branches ramify through the ages until it is no longer possible to be sure who the current coheirs are, the title is called dormant.
Any I've forgotten?
My source for most of my knowledge of heraldry is the admirable A.C. Fox-Davies, A Complete Guide to Heraldry, 1909.