"tty" originally meant "teletype" and "pty" means "pseudo-teletype".
In UNIX, /dev/tty* is any device that acts like a "teletype", ie, a terminal. (Called teletype because that's what we had for terminals in those benighted days.)
A pty is a pseudotty, a device entry that acts like a terminal to the process reading and writing there, but is managed by something else. They first appeared (as I recall) for X Window and screen and the like, where you needed something that acted like a terminal but could be used from another program.