Time Trial bars on regular track frame?
 

Horribly noob question, but is the only difference between a typical track bike and a TT track bike the bars? The Look T20 TT and Speed editions seem to have identical stack, reach, and HT/ST angles. I kind of expected that a TT bike might have a super-steep ST angle like a tri bike, but I guess not? And if the bars are the only difference, can you just swap cockpits for different events?

Yes. The TT version comes with the TT bars. The Sprint versions do not.

The aerobars are generally pretty pricey to buy on their own, and a lot of people do not want or need them, as they already have a nice set up. And yes, you just switch cockpits for the events.

Some companies will claim that there is some difference in the carbon layup of the two versions, and in some cases there may be, but it's not going to matter for any amateur.