Well, I have to admit that I don’t often see these two mixed up as such, but because they look quite similar, there is a need, in my opinion, to have a quick and easy way to distinguish them laid out. And that’s what these Troublesome Pairs are for, after all. I do monitor how many searches I get on the pairs, and it’ll be interesting to see how many people search for these in a search engine and come through to here. (If you have a website or blog, statistics are your friend, and can give you surprising results, too!)
Homogeneous means of the same kind, consisting of parts all of the same kind (it is also the name for a chemical process involving substances in the same phase, i.e. all liquids or all gases, if that helps you remember it). It comes from the Greek for same race or kind. Yes, the same as homosexual. The way I remember this is that homogenised milk is the one where the cream is mixed into the milk rather than sitting on the top (that made me feel a bit nauseous for a moment, as I only drink skimmed milk, myself!)
Heterogeneous, on the other hand, means diverse in character or content (a heterogeneous chemical process is one involving substances in different phases, e.g. mixing a gas with a liquid, in case that helps you remember). It comes from the Greek, again, for other race/kind. And, yep: heterosexual.
Note the spelling, by the way: -geneous, not genous. Not even if you’re in the US, I believe.
So a word pair and a pair of prefixes defined for you today: extra value!