The shower head’s thread
In the US and Canada, a shower arm has 1/2" pipe thread on the outside. Kohler’s K-7397 arm is 1/2"-14 NPT at both ends, and Moen and Delta label their heads’ connection 1/2" IPS or standard 1/2" pipe. The head screws onto the arm, so its inlet takes a 1/2" male pipe thread.
Shower head makers disagree on tape. Moen’s instructions wrap the shower arm with thread seal tape, Delta’s sheet for one of its heads says tape can cause product failure, and Waterpik tapes metal connections only. The adapter’s male thread takes the arm’s place.
In the UK, Australia and New Zealand, shower heads use 1/2" BSP instead. See shower head thread size.