SSD would be a type of hard drive. As the initials suggest, SSD is a solid state drive so there are no moving parts. Other drivers have a mechanically spinning disc (e.g., SATA drives). SSD drives were once MUCH more expensive than the SATA drive and its predecessors. But, cost have come down so they are reasonably priced too. The SSD drive can be expected to be more reliable (less prone to failure). Even so, it makes sense to have back up drives to save your music so that if the drive goes down you have not lost your music.
My local audio dealer who was also a computer guy, said that SATA discs might be less electrically noisy, and therefore better for music storage, but, that was quite a while ago and I would bet the SSDs are better now.