What differences will happen if you use a rectangular baker to bake cookies instead of a tray?
They should be fine.

It's possible that they'll be a bit gooey, or just a touch underdone.  The high sides of the pan may shield the cookies from the heat, just a little bit.  The glass pans will absorb a little more heat, and so take just a tad longer to heat up - partially balanced by the fact they take a tad longer to cool down, and so might carry over a bit of residual cooking.  Both effects should be pretty minimal, but cookies do bake for a very short amount of time, so the difference may be noticeable in a way that longer-cooking dishes would never notice.  

If you look at your cookies, instead of just pulling them out when the time is up, you should notice if they need a touch more baking (I would guess maybe a minute of extra time, if any)... of course, you should probably be doing this anyway, especially if you want to cook them to your desired style (if you prefer a bit softer or a bit crisper, for example).  Light browning on edges or ridges should be a very good cue for done-ness.