"Often the transmitter will come with a lavalier (lapel clip-on) mic, but you need to purchase the headset mic separately"
In most I've seen advertised, you choose which type of mic you want when you buy the system, so if you want a headset you choose that as part of the whole kit. But it's true that headsets and lavalier kits use the same belt pack transmitter: it's only the mic that's different.
A handheld mic is different. It doesn't use the beltpack: then the transmitter is built into the the mic.