Hi voxware,
A headboard and footboard are optional items that are mostly for looks or to fit the decor of your bedroom and you would need to choose these separately (if you want either one at all) based on your preferences. They generally attach to a bedframe.
You can use a foundation directly on the floor but most people would prefer more height which is why they are usually used on top of a steel or wooden bedframe. You could also attach legs directly under the foundation such as the bedlegs here so you wouldn’t need a bedframe as long as there is a way to attach them securely to the foundation and have legs in the center for good center support to the floor (see post #1 here). There may not be a way to attach a headboard and/or footboard directly to a foundation (if you prefer them) since these are usually attached to a steel bedframe or are part of a wooden bedframe.
Another option would be one of the wire grid platform foundations similar to the ones that are listed in the foundation post that are a bedframe and foundation in one as long as your mattress doesn’t have a latex support core which may sag into the gaps in the wire grid over time (see post #10 here). You can attach a headboard to most of these.
You can also choose a platform bed with a slatted support surface (some of which come with a headboard and footboard that are part of the bed or are optional additions) or even with a solid support surface (see post #10 here) that doesn’t need a foundation as long as the distance between any slats in the support surface is suitable for the type of mattress you have. These are more of a furniture item and tend to be more costly.
All of these would be a suitable choice and would depend on your preferences and budget.
Phoenix