The term "file system" in computers (at least in Linux) is ambiguous.
It has a generic meaning to describe the design approach taken to organize data on a given partition (physical or logical), e.g.,
- BTRFS
EXTx
FAT
ZFS
BTRFS
NTFS
With this meaning, I would say these refer to the software used to organize the data stored on a partition.
On the other hand, the term is often used to refer to some collection of storage which may or may not be mounted. The "collection of storage" may be a partition on a hard drive, but it may also be a logical partition comprised of a collection of who-knows-what across a number of hard drives, as provided by something like mdadm or a network storage system. The storage will have been formatted using a given "file system" (such as EXT4), but after that the storage itself it then referred to as a file system, and which may be displayed in Linux using the df command. In this use of the term, it refers to a specific piece of storage and it is clearly not software.
Maybe I'm the only one who finds this confusing. (For some time, it annoyed me. Eventually I realized that resistance would be futile.)