Yes, and in the case of a closed timelike curve, the laws of physics won't let you do something different the second time you are at a particular event in spacetime than you did the first time. Both are straightforward constraints from the point of view of the laws of physics.

But that still does not mean they look the same to us, intuitively speaking. For example, the laws of physics won't let you walk on the ceiling at all, whether your worldline is a closed timelike curve or not. But if your worldline is not a closed timelike curve, then, intuitively, it seems like the laws of physics will let you choose which direction you want to walk on the floor. However, if your worldline is a closed timelike curve, and you come around again to the event in spacetime where you chose to walk to the left last time around, the laws of physics will not let you choose to walk to the right this time; they constrain you to walk to the left again, since from the standpoint of the laws of physics you are at the same event in spacetime and that event can only happen one way. To many people that seems like a much stronger constraint than the constraint that you can't choose to walk on the ceiling.