No they are not: F-Droid builds a signs the apps independently. Source: I have apps on both stores.

All F-Droid apks are signed with a different key than the play store one: you do not upload your key when you publish on F-Droid and all the apps are built from source by the F-Droid build servers.

Interesting. But should this apply to many apps on F-Droid? I also have an app published on both the Play Store and F-Droid and I don’t recall having seen requests to change the application ID to avoid clashes between stores.