Difference?

From my rather ancient viewpoint lip synching was the process of putting a voice onto film so that it looked as if the picture and sound had been recorded as a piece. Often necessary if there was extraneous noise when filming on location or in a musical number to permit cuts between different shots.

Miming is simply pretending to perform live as on ToTP. I remember seeing a band stop playing several seconds before the recording finished on one occasion.

Like many terms people are lazy and start to use them interchangably.