About imperial princess vs princess, I take that you've known of the Chinese title Huangdi which is translated as "emperor" in English. "Imperial princess" (皇女), literally, means an emperor's daughter. Likewise, the word "princess" (王女) here means a king's daughter. They by themselves aren't titles and just words to call. The title of princess, on the other hand, is generally referred to as 公主 (gongzhu). It is a title, like dukes, counts, etc. and must be granted by the monarch, not something you're naturally born with. To avoid calling their real names, unlike in the West, princesses would be called by name of their fiefdom or a fancy word + the word 公主.