There's a wee bit more difference between the two: when a person dies uncleanly, their body's pyreflies - their spirit and essence - get twisted into a fiend. The aeons, however, are temporary projections of the spirits trapped in the fayth statues in the temples. The fayth used to be summoners (a different kind of summoner, presumably), but they allowed their powers to be entombed inside statues for future use once Zanarkand was lost.
The general principle of aeons and fiends is similar, in that they're both powerful entities created out of spirit energy, but the way they actually work is quite different.