* Friction is a force that opposes motion. It's always there, whether an object is moving or not.
* Static friction is the force that keeps an object at rest. It's the friction that prevents a book from sliding off a table, for example. It's not zero, but it's just strong enough to counteract any other forces trying to start the object moving.
* Kinetic friction is the force that acts on a moving object, slowing it down.
So, to answer your question directly:
* Frictional force DOES act on objects that are not moving. It's called static friction, and it's what keeps things from moving in the first place.
Think of it this way: imagine you're pushing a heavy box. You push with a little force, but the box doesn't move. That's static friction working against you. You push harder, and finally, the box starts moving. Now, the friction is kinetic, and it's trying to slow the box down.
