Where would my Poohian Theocratic Republic fit on the list?

HEIL HONEY!!!!

This was an interesting take.

In reality though you could have a democratic republic or an Oligarchic republic, depending on how the people who make the laws get put into position. Here we usually elect them by popular vote at some level.

The US also has the Federal versus State laws/rule, which will eventually end up in the federal courts to decide if constitutional.