Numbers of each system are independent, so they run through the same numbers. FM/RMs go to the highest number, currently 3541.
Farm-to-Market and Ranch-to-Market are a single system and share a number pool (there won't be FM 10 and RM 10).
Loops and spurs, a subcategory of state highways, are a single system and share a number pool, separate from state highways. Park roads, a subcategory of the loop/spur system, are separate. Recreational roads are also separate. There's SH 10, FM 10, PR 10, Rec Road 10, and Spur (SS) 10, but not Loop (SL) 10.
The exception is FM/RM spurs. Those are numbered the same as the FM or RM they spur from. They're signed with the regular spur sign, but are designated along with the parent route, not separately.
Ranch Road 1 and NASA Road 1 are the only ones of their type. As far as I'm aware, Beltway 8 is a custom designation of Loop 8 and is the only one of its kind.
Business routes of state highways, US routes, or Interstate highways are all state highways. Each is signed and numbered according to its parent route. I think FM/RM business routes stay on the FM/RM system.
There's also a mysterious PASS (Principle Arterial State System) category. They're not of interest to drivers; I've never seen one signed. I've only seen them on official maps and descriptions. Most of them follow urban city streets, but a few follow urban on-system roads. I assume they get some kind of supplementary state funding. They're numbered differently, based on location, from the 200s in the Fort Worth area to the 2400s in the El Paso area.