Why do "prisoner" and "jailer" mean different things?
Solution 1:
The short answer would be that jail may be used as a verb, but prison is verbed only in archaic poetry (imprison takes its place in ordinary modern speech). People may be jailed, but who ever says they are prisoned?
Solution 2:
It looks to me like the distinction in meaning between prisoner and jailer was already present in the French ancestors of these words. The word prisoner in the sense of "occupant of a prison" seems to be derived from the French and Old French word prisoner/prisonnier.
The noun and adjective suffix -(i)ier in French (derived from Latin -arius) seems to be used somewhat differently from the suffix -er in English. While English -er nouns mostly refer to agents of a corresponding verb, French -ier words often seem to be based on nouns, and refer to someone whose profession or location is related to that noun. For example, the French word caissier (the source of modern English "cashier") is derived from the noun caisse "box/cash register", not from a verb. It doesn't mean "a person who cashes", it means something like "the person associated with/located at the box (where money is kept)".
The Wiktionary entry on -ier in Old French says that one of its uses was to form nouns that "[indicate] location, where one lives". So I think prisoner can be explained as referring to "a person who is located in/lives in a prison".
The word jailer/jailor/gaoler, in contrast, seems to have had some influence (as the -or spelling variant implies) from a French word with the French agent-marking suffix -eur (derived from Latin -or). Now, I don't think this is necessarily very explanatory, since it seems the forms with -eur showed variation with forms in -ier in French. (In fact, the form used in Modern French has -ier: geôlier). But I think it may play a small part in the explanation for why jailer didn't develop the meaning of prisoner. Despite the apparent similarity in form between these words, their etymological sources are not entirely the same. (The other part of the explanation may simply be that -ier in French has a broad enough meaning, or at least did at the time these words were formed, to encompass both of these meanings.)
Once these words had entered English, the (apparently pre-existing in French) distinction between their meanings would likely have been reinforced by the fact that, as Robusto observes, jail is more commonly used as a verb than prison.
According to the Oxford English Dictionary (OED), there are (seemingly rare) examples in Middle English of the word prisoner being used to mean jailer/jailor/gaoler:
- a1325 (▸c1250) Gen. & Exod. (1968) l. 2042 An litel stund quile he [sc. Joseph] was ðer, So gan him luuen ðe prisuner.
- c1450 (▸c1405) Mum & Sothsegger (BL Add. 41666) (1936) 1251 (MED) Pouerte hath a pressonere whenne he doeth passe bondes.