Will my 2002 Subaru Impreza Outback Sport motor (2.5L) work in a 2000 Impreza Ouback Sport?

unless the 2000 had the same motor and trans you'd have to swap the motor, trans, and the wiring harness. if it was the same 2.5L motor then it would be a direct swap.

Actually, in this case, you can get away with swapping the long block, but you'd have to retain your electronics. You'd also need to swap all sensors and gears on the timing, including crank gear, crank sensor, cam gears, and cam sensors, but then it would work. It's a little more involved than simply dropping right in, but at least you don't have to swap the trans and wiring harness.

Is a 2002 Impreza outback sport 2.5 engine the same as a 2002 Impreza ts 2.5 ?.

Sedonkid. I don't see any issues with that swap.

Awesome thank you Cheers