Does Miss and Ms. fit under the category of homonyms or homophones, or are they under another category?

They are not pronounced the same way, at least in most parts of the country.

Miss = mis

Ms. = miz

so what is their category? Can you give me another example of this?

Homonyms share the same spelling and the same pronunciation but have different meanings.

http://www.editingandwritingservices.com/homonyms.html

http://en.wikipedia.org/wiki/Homophone

Miss and Ms. are titles, just as are Mrs. and Mr.

those were just examples, so they are homographs?

They are not homographs. They have different sounds, different spellings, and different meanings.

http://www.dailywritingtips.com/homograph-examples/

Can you give me another example that is similar to MIss and Ms. ?

The only connection I see between Miss and Ms. are that they are titles: Dr. Mr., Mrs.

Many short words start with mi: mid, miff, Mig, mil, mitt, mix