I call this part of sound design "building a sound vocabulary" or a "sound language," with which specific instances of sounds can be used that all family well together, as if voiced bt the same object or character. (Seems like this is something that's even more critical in non-linear media like games, perhaps moreso even than film, so I'd love to hear more thoughts from the game sound designers here on SSD...)
If it's synthesized, I use LFO's and other kinds of modulation, usually subtle, recording or printing many takes. [edit: the LFO's or other modulation are set to affect pitch, EQ, filtering, and/or dynamics, based on the context and needs of the sound or action being shown]
If it's based on real-world recordings, I do obsessive amounts of takes with way more variations than might seem advisable. When I get back to the studio and critically listen, the number of usable takes dips dramatically, so over-covering a sound source winds up yielding just the right amount of usable variations. Do this enough, with enough different layers, and these sound languages can be varied but sonically unified. I tend to stick to simple dynamics and EQ tools to even things out, instead of using heavy processing, to keep things sounding organic.
[edit: Since you mentioned dinosaurs and variation...] Randy Thom has said that the thing that impresses him the most on a demo real are emotive creature vocalizations, because that's one of the hardest things to do. Having tried it once or twice, I'd have to agree. Designing a happy sound, a curious sound, and an angry sound for the same creature can be damn tough. But it's like magic when it's pulled off well.