In SQL Server, the full-text catalog is a logical concept and does not reside in a filegroup. Therefore, to back up a full-text catalog in SQL Server, you must identify every filegroup that contains a full-text index that belongs to the catalog. Then you must back up those filegroups, one by one.
When a full-text index is created, it is placed in one of the following locations:
A user-specified filegroup.
The same filegroup as base table or view, for a nonpartitioned table.
The primary filegroup, for a partitioned table.
If the database has full text catalog, you'll need to backup the filegroups pertaining to it. It is possible that there is a filegroup only containing the index for the full text catalog and nothing else, as seen by "A user-specified filegroup".
If a full-text index resides in a separate filegroup from all of the associated table data, the behavior of piecemeal restore depends on which of the filegroups is restored and brought online first:
Now for filestream, you can see an example of backups and restores here:
You can see that the filestream backup data is classified as type S as you talked about. It is also seen in SQL as FILESTREAM type and is it's own file to be restored.
To recap, you may run into F and S type in the filelist. S type seems more likely as it's possible the full text indices reside in a filegroup with tables or other data and would be seen as D. You can specify your own filegroup for full text indices that contain just the indices however.