btx is a different kettle of fish, and doesnt necessarily mean a case will be a desktop style vs a traditional tower (btx and atx come in both format)
Balanced Technology eXtended is a lot more than a case...it is a different motherboard design, case, power supply and thermal module combination. Sure, you cant stuff and atx board in a btx case, not can you stuff a btx mb in an atx case, but btx is not a case as such, it is a specification, the same as atx is/was.
Just coz the case is on it's side doesnt make it atx or btx, it makes it a case.
If you come across a btx motherboard, it will be easily recognisable because it looks backwards...the cpu socket is centrally located and the pci/pci-e slots are on the "wrong" side.