I think Thee would be for family, friends, or someone of equal social status and thou is more formal (but much less used now - only as tha: “tha's gonna get it“).

That's fascinating , because it's originally a subject/object divide (equivalent to he/him)

Definitely a formal/informal distinction.

Old Yorkshire phrase for telling children to mind who they address as 'thee / tha': "Don't thee tha them as thas thee" - kind of a similar sense as 'mind your Ps and Qs'.