Backups & restore points · Time Machine and backup strategy
Can I keep my backups on the same external drive I move files to?
Short answer: You can back up your Mac's internal folders to it, but not the fast drive's own contents — they'd share a drive with their backup. Give the Fast drive working set a different destination.
You can back up internal folders to it, and that still protects them against mistakes and against your Mac's own disk failing. But don't use it as the backup destination for the fast drive's own contents — the files you moved there would then live on the same drive as their backup.
For what's on the fast drive, give the built-in Fast drive working set a different destination: another drive or a cloud account.