1. Sprite Packer (pro)
2. Sprite Editor (free)
They do different things. Actually they kinda do the opposite things of each other.
Sprite Editor (free) is in the import pipeline. It takes texture as input and has sprite assets as output. Say you have ten sprites all on a single texture, Sprite Editor allows you to visually define where those sprites are (UV rects basically) and then import pipeline will spit out ten sprite sub-assets. You can then use these sprite assets in your game. We also offer something called automatic slicing or grid slicing in the editor, so that it is very fast operation workflow-wise. You can define these rects via the texture importer APIs too.
Sprite Packer (pro) however does the opposite. It takes sprite assets as input and texture sheet as output. When you have pro, it doesn't really matter how you import your sprites (as singles or sheets), they will get repacked (unless you tell Unity you don't want to) when you build or when you go into the playmode. The result will be tighter than typical rect packing. Sprite Packer has no script APIs at the moment.
So if you only have free, you need to have your sprites already in an texture atlas. You then use Sprite Editor to slice. If you happen to already have the metadata where the UV rects are, you can also create your own importer that spits out the sprite assets automatically.
I think the bottom line is that with free version, you can import atlases, and it's easy to slice them to assets. For 1 sprite = 1 texture, you can make the packing yourself, but you need to operate on rects. With pro, you get automatic packing that doesn't really require any effort on your part and has the tightest packing evar.
To clarify: Sprite assets are always sub-assets of a texture asset.