Albums and Collections are essentially the same thing, it's just that Adobe chose to use different terminology when developing the Lightroom app....so Collections in Classic, Albums in Lightroom are the same, i.e. a list of images assigned to a specific Collection/Album. The images themselves are physically contained in folders in Classic, which the user can see and access via the Folders Panel (along with the containing drives), and while they will be similarly stored on drives in the Cloud servers the user doesn't get to see those drives. Compounding the confusion even more is that the term "Folders" is used in Lightroom to represent the equivalent to Collections Sets in Classic, i.e. a "Folder" in Lightroom can only contain Albums (or sub-Folders) in the same way that Collections Sets in Classic can only contain Collections (or lower level Collection Sets). Neither Collections Sets in Classic nor Folders in Lightroom can directly contain image references.
Regarding your last bullet point, I would guess that when you imported those 520+ images into either Lightroom or LrClassic you had (presumably inadvertently) the "Chair" album/collection designated are the album/collection that the imports were to be added to. That's an optional import setting which you presumably didn't notice had been set. So check the import settings next time you import into whichever app you are currently using.
As you have a copy of the excellent Missing FAQ book, I suggest spending some time reading the "Cloud Sync" section, which will explain much more thoroughly how syncing works, especially when choosing to sync Classic with the Cloud.