Let’s get something straight here
Punch wizard: Mage/primary caster that punches people, typically to apply spells and/or as their primary melee option
Example: Alex Louis Armstrong (Full Metal Alchemist)
Fistomancer: Overly adamant Bigby’s hand users and/or a caster that summon fists/punching spirits/other punching forces to bludging/beat up/decimate foes.
Example: Jostaro Kujo (JoJo’s Bizarre Adventure)
Punchlock: Warrior who is only able to rely on unarmed combat either through some vow, deal, arcane curse, or other means in which they do not or cannot use weapons.
Arcane fist: A warrior who uses their fists, though not necessarily without weapons, mixed with (typically arcane) magic as their primary method of combat. Typically will delivers spells by punching.
Example: Yang Xiao Long
Muscle Wizard: A wizard with high strength, beautiful muscles, and often high charisma, who uses their displays of strength for unorthodox solutions and/or diplomacy
Example: Alex Louis Armstrong (again)
See also: Pipe organ bard
Mind you, it should be clear that these are not exclusive terms. As it stands, Ro is a punchlock/arcane fist and mixing styles is completely allowed. There’s also the unarmed magus, which is exactly as it sounds, the celestial timebomb, and the bear puncher, which is a druid that turns into bears or other animals and punches things (I know it’s confusing).
Glad we could clear that up. Please let me know if I missed anything.