Are they commands or utilities?

I'm trying to figure out the correct term(s) for Unix/Linux "commands." Specifically, I have always understood that technically *commands* (e.g., cd) are built into the shell, and that other "commands" (e.g., rm, ls, mkdir, cp, mv) are better termed *utilities*, as they are stand-alone programs. (As far as I can tell, rm, etc. are all in /bin.) Furthermore, one way to tell whether something is a command is to see if it has a man page: commands don't, but utilities do. However, all of the sources I've found via Google use "commands" exclusively. Can someone set me straight on this or point me towards an appropriate reference? Since exit doesn't have a man page and isn't in /bin, is it, like cd, a true command?