For the $300-$400 dollar range, you’re not going to get an instrument with weighted keys (ie, feels like a piano). Maybe this is no big deal to you, but unless the specs say “weighted keys,” you’re just going to get light keys with no weight or resistance.
As for the difference between the two Yamaha keyboards, from the Yamaha website, here are things they say the 202 has that they don’t mention about the 200:
32 notes of polyphony - since they don’t say anything about the 200, I’d imagine it may have 16 notes of polyphony. Could be an issue if you want to pedal anything.
MIDI IN/OUT connectors and is General MIDI (GM) and XG Lite compatible, critical for computer use - now, it does say the 200 can be connected to the computer, but I’m suspicious about the fact that it doesn’t mention MIDI in/out for it. If you’re not concerned with computer hookups, don’t worry about this though.
Something like this would give you a much more real piano feel, but it doesn’t come with onboard sounds, speakers, a stand, and that sort of thing. Much more of a hastle, but with this one at $230 on sale, I’d imagine your total cost’d be somewhere around $800 (for example, you’d need something like this as a sound source, maybe this as a speaker, and then probably a $40-50 dollar keyboard stand (which you’d need with the other one too, unless you wanted to just put it on a table) and maybe the same amount in cables.
So, it all depends on what you want. If you’re fine with a non-weighted, very portable and self-contained keyboard, I’d go with the Yamaha 202. Be sure you know you’re ok with non-weighted though. $300-400 is a lot to waste on something you won’t be happy with.