Atoms move at different speeds depending on whether they are in liquids or solids because the atoms or particles in solids are closely bonded while they are loosely bonded in liquids.
The attractive forces between the particles are so high that they remain in fixed positions. The particles, then, cannot slip over the neighbors particles. They can only vibrate. That is why solids have definite form and volume.
That the particles in liquids are loosely bonded means that the attractive forces are less compared with solids. Then the partilces can move and pass each other. They are not in fixed arrangements any more. Yet the particles are attracted to each other, so they have definite volume, although they take the form of the vessel, and they can flow.