Actions are things you need or want to do. Checklists are reference lists that may help you accomplish actions, steer projects or determine what actions or projects you need to have.
One example of a checklist is a list of items to pack when you travel. It's pretty simple and something you only refer to when you're packing.
As Oogie has already described, you can also use checklists to help you manage projects that tend to recur and have the same sequence of steps, targets to hit or what have you.
Regardless of how you manage your AOFs and higher level horizons of focus, these are ultimately just checklists you review periodically to for ideas about projects or actions you might need to undertake.
Checklists can also be kept on hand to help with fun things. For example, you can keep lists of things to do when you're in a certain place, wines you like to buy, or movies you may want to see when the opportunity arises.
There is no one set way you need to manage checklists, but in my system I like to keep them managed separately from projects, actions and the like. Even though checklists can help with actions and projects, they're not the same and I try not to treat them as such. But they're yet another tool to help you keep things off your mind.