The Kirin & the Qilin are the same thing. Even the characters are the same. But, over time Japanese culture made variations of styles, as did the Chinese.

The characters at the top are written "backwards". The one on the right is "Qi" (Tchee) the Female (or spoken as "Ki" in Japanese), then the one on the left is the male "Lin" (Leen) and sometimes pronounced "Ling" (or spoken as "Rin" in Japanese).
(Some people call them the other way arround as the Lin as female and the Qi as male. In fact I just read a story where they did that.)

The stamps:

The left stamp is my "Name" stamp, which is "Ren Si Qi" with the same charecter "Qi" as in the Qilin, and my name means: Surname: "Ren" "Task" or "Duty" (depending on the translation or usage of the word) Personal Name: "Si Qi" "Thinking about the Qi" or "Pondering the Qi" or "Thinks about the Qi"

The stamp on the Right corner is what is known as a "Slogan" stamp, or "Poetry" stamp. It says: "Art is the Color of my heart." which is also written "backwards" and from top to bottom. It's actually more of a modern concept tho' and wouldn't make sense in ancient times...

Then the little stamp, is a more modern type of Chinese stamp with a logo on it. i tend to see these often times with English written words, or with Russian. (Can you believe that?) It says "Wu Du Jiao Shou" Meaning "Dark/black Unicorn/1-horned Beast" since there's no actual word for "Griffin". Some people use "Vulture" but it's WRONG!

Hope that helps. :D