My old motor was a GE 1075rpm, 1/6hp, model P870S
My 3 wires are black, brown, purple.
My new motor is GE 1075rpm, 1/6 hp, model R367S
Those 3 wires are black, brown, orange.

Are orange and purple the same?

My purple went to one of the connectors on my capacitor. Does the orange connect at the same place?

The orange and purple are usually the same but the brown wire is the one that should be going to the capacitor. Unless the purple wire was going to the terminal that also has a wire going to the contactor then the brown wire would still go to the cap on the terminal marked fan. The orange / purple wire uses the same side of 220 volt as the brown wire to start the motor so it should be on the common side of the cap. I'm guessing the cap has 3 terminals correct?

the orange and purple are usually the same but the brown wire is the one that should be going to the capacitor. unless the purple wire was going to the terminal that also has a wire going to the contactor then the brown wire would still go to the cap on the terminal marked fan. The orange / purple wire uses the same side of 220 volt as the brown wire to start the motor so it should be on the common side of the cap. I'm guessing the cap has 3 terminals correct?

My capacitor does have 3 terminals. At around 8 o'clock that wire is yellow. At midnight, is where my brown wire was connected. Then around 4 o'clock that terminal had two wires. My purple and an orange going to another direction than to the fan motor.
My motor model is P870S. The replacement is R367S.
The only difference, since both are 1/6 hp and 1075 rpm is the purple vs. orange wire, and the thickness of the R motor. It mounts using a belly band and mine is a stud mount. So, the bolts on the replacement motor won't work. I did find a guy with loose parts and was able to get 4 of the 4 1/4 inch bolts so I can mount the R motor using the studs. If the orange wire and purple are the same (since black should match black and brown should match brown) then I may be good to go. Thanks.