Apps (apks) must be signed before uploading to distribution sites like play store or f-droid. Some devs are signing their app releases with different keys, because for example the google play version of the app has to contain stuff they don’t include in f-droid versions. These are mostly privacy related things, google does not allow in their play store. In case of bitwarden the two versions are most probably the same and they’re signed with the same key. So if there’s an update in either of the two distribution sites it will show you, that there’s an update. Now I use Aurora Store instead of play store for apps that are not available in F-Droid and you can blacklist apps there, so I only get updates from F-Droid.
No, the opposite