Suppression temporarily deletes an object (feature in a part, component in an assembly) from your model. Since it's temporarily deleted, Pro neither regenerates nor repaints the object on your computer screen. Since the object is temporarily deleted, it has an effect on parent-child relationships. You will have to tell Pro how you want to treat the children (delete, suppress, edit definition, edit references), or your model will fail regeneration (Resolve Mode).
Hide is a functionality added in 2001 that only removes objects from display. In part mode, you can only hide non-solids (e.g., surfaces and datum features). In assembly mode, you can hide components. It has no effect on regeneration. In essence, Pro creates a layer called BLACK HOLE, and the objects associated to that layer are blanked.
To get a suppressed object back, resume it either by selecting it in the model tree, right mouse click, and Resume, or use Edit > Resume. To get a hidden object back, use right mouse button functionality, or View > Unhide (or is it View > Visibility > Unhide; I forget).
As I said above, in part mode (or more precisely, for features), Hide only affects non-solids, and does not affect solid geometry. (Just like layers.) Therefore it only affects surface features and datum geometry. If you hide a solid feature that has datum geometry (e.g., the axis of a hole feature), only that datum will be affected.
Here's the important part: Hide is only intended as a quick way of reducing screen clutter without having to go through the process of creating and blanking a layer. It is intended so that a user can quickly use right mouse button functionality to get junk out of the way when working on other features and components. Again, only temporary -- once you're done with your operation, you should unhide those objects.
(In 2001, you could not save Hide settings; they were reset each time you started a new Pro session or cleaned out your RAM. If I'm not mistaken -- and this disturbs me -- your Hide settings are saved with your model, which can make it a pain in the butt to figure out where stuff is when you open it.)