It's amazing what you learn when you re-read things.
From Harris - because g.t.q. was so formal (and slow), less formal scripts were developed a mixture of g.t.q. and cursive hands.
These were generally known as 'Bastard' hands.
The French formalized version was "Batarde" - hence all my confusion about Bastard vs Batarde.
The German versions were Fraktur and Schwabacher
The Italians got into the Rotunda form.

It's a lot more complicated than that, but there's a start.