To cease. A stop is an ending that could have continued, which is what distinguishes it from finishing.
Late Old English stoppian (to plug, to stuff up), from a Germanic borrowing of Latin stuppa (coarse fibre used to plug a hole); an ending that could have continued was first, quite literally, a hole plugged shut.
Ceasing, in a way that could have continued, which is what separates a stop from a finish. Even the oldest sense of the word was a hole plugged, not a task completed.