Specific to this topic, for a long time now both common parlance and editorial stylebooks have accepted “bullet” as a colloquial synecdoche for a firearm’s cartridge or round.
Since the most important thing in this topic to you is pettifogging dictionary definitions, allow me to introduce and define some other concepts with which you seem to be unfamiliar.
Hope you found this comment as helpful, informative, and germane to the discussion as I found yours.