What is the difference between an object at rest and an object in motion?

Reading up on basic Newtonian physics I know that an object at rest stays at rest unless acted upon and I know that an object in motion stays in motion unless acted upon as well. It seems weird to me that one object can be still and one be moving without any big differences in relation to time, mass, energy, gravity.

I guess what I'm asking is if there are any drastic differences from an object sitting perfectly still in an empty space-time and an object moving at a constant velocity through an empty space-time.

Is there a minimum speed limit with respect to the fabric of the universe (not in relation to earth)