Varies by design. Some just as you describe (many rifles are push feed and therefore have no claw). Some rotary magazines have a release button.
My Mauser has a floor plate but I unload it like a blind anyway, just gently pushing the bolt forwards enough to take the cartridge and back across the ejector. Very safe as the round is never chambered.
@alberta boy suggested this method to me and it works.
The floor plate is useful for inspection and cleaning but for hunting purposes I would probably choose a blind mag for strength all other things being equal....