What is the difference between 山顶and 山巅? What is the difference between these two words?  Is there any difference? Are they used in different regions?
Yes, they are both peak.
For me, 山顶 is more general word for peak. But 山巅 is more powerful, usually is used in  the literature.
You can say 山顶 for a hill or a mountain, but you don't know if there are other higher 山顶s around. But 山巅 is supposed to be the highest among the nearby region.