The differences between different kinds of cheese depend on a whole bunch of things, including what exact cultures are used, what temperatures and for how long, how the curds are cut and stirred-or-left-to-clump, whether the curds are rinsed (some whey replaced with warm water, to let curds set in a less-acidic solution), etcetera. All these factors affect the cheese's taste, texture, creaminess, ageing characteristics, etc. In a very complex and near-incomprehensible way IMO
The issue of what "defines" cheddar (or colby either for that matter) is probably not something you want to get into -- it will make your head hurt

And it depends a great deal on WHOSE cheddar (or whose colby) you are talking about, as grocery-store type cheese is labelled as far as I can tell as a PR thing rather than necessarily reflecting a particular manufacturing process.
But if you really want some sort of answer, overgeneralized though it is: In principle, the "truest" cheddar involves a particular method of cutting, draining, and repeatedly inverting the curds in a big block; and I believe the curds are normally not washed. And in principle, colby does not involve this true "cheddaring" process but does involve washed curds. Otherwise however they are not all THAT unalike in how they are supposed to be made, at least not as dissimilar as either of them are to (say) Brie or mozzarella or swiss.
I have no idea what if any legal controls there are on what mfr's call cheese; it sure seems like for plain ol' cheap cheese from the supermarket (as opposed to fancy imported or artisan-type cheeses) the mfr can call it pretty much whatever they think will sell it
Pat