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Generally smoke is a bad thing, indicating a motor has seized up or is about to. And then if a breaker doesn't trip, you have a fire.
It *could* be the motor had something in it (bugs, mouse nest) that has now been burned off but I still wouldn't trust it without eyeballing the whole thing real close, or getting it out to a motor shop to see if it needed overhaul. Could be you just "burned off" a problem area in the insulation or coils in the motor--leaving a raw spot that will cause more trouble in the near future. (Motor, blower, whichever.)
Electric-driven compressors generally are sealed and won't make smoke. Bottom line is, you need eyeballs in there to look for the charred parts before you can use it with both eyes closed again.