HP - when was it used and why?

So did the car you ordered and the engine in it dictate if it received an "HP" engine?

For example, my 67 A body came with a 383 that was not stamped HP, but yet it received an HP engine?
I've heard of A body BB cars with the HP and without.

If I ordered a 68 Road Runner with a 383, that would be an HP engine as well, based on the car and engine combo I ordered, correct?

And in either case, HP may or may not be stamped on the engine, yes?

I'm not looking to make a big deal about HP engines, or HP2 engines, or the lack of the designation- I am trying to figure out what customers would, or could order, and how the factory workers new what to mark HP, or if that was random, and how they knew what engine to install on what car?

I find this stuff very interesting, and it makes me wonder 'where are the assembly line workers today?'
I'd like to pick their brain.