On Wikipedia, I started from the page of Ramses II, who is described as a pharaoh, and kept clicking on the 'predecessor' link. Every predecessor was a pharaoh until I got to Ahmose I.
Ahmose I is also listed as a pharaoh but the page shows that he had two predecessors, Kamose and Khamudi, both of whom are listed as either 'king' or 'ruler' instead of pharaoh.
The predecessor pages of both Kamose and Khamudi omit the title of pharaoh for several generations. I didn't go too far up the Khamudi predecessors, but the Kamose predecessors are all listed as kings up until Sobekemsaf I, who is listed as a pharaoh.
Sobekemsaf's predecessor, Rahotep, is also written as a pharaoh, but my predecessor search ends there as there is no predecessor link on his page.
Rahotep is in the 17th Dynasty. I checked some previous dynasties, and it appears that all the prior rulers were called kings, up until the 13th Dynasty where they are called pharaohs again. I stopped searching here because I'm guessing going back to the 1st Dynasty will have similar results as switching back and forth between king and pharaoh.
So, my question is, what exactly is it that makes a pharaoh and how does it differentiate from king? In other words, why aren't Kamose and Khamudi listed as pharoahs?