If electrons exist as a probability distribution then in what sense do they move around the atom?

Very likely some of my understanding here is wrong, so I'll try to clearly restate what I think I've heard physicists say.

1. Electrons exist as a probability distribution around the nucleus of an atom so that we cannot say where they are located but only give a likelihood of them existing in various places.

2. Electrons move around the nucleus at some speed.

These two conceptions of electrons seem to contradict each other.