A Professor is an academic  an academic rank at universities and other post-secondary education  institution
How are professors different from teachers at k-12?
Yes they are, the name was derived from Latin as a "person who professes" being usually an expert in arts or sciences
So professors must have more education than teachers.  Do professors have an opportunity to advance?
Yes they do. Usually the position only refers to the most senior academic position which means they have progressed
Do some move on to become Deans of colleges?
In USA, the word professor is sometimes used colloquially to refer to anyone in an academic post.
Oh so deans are included in the term professor.  How would I become a professor?
For you to become a professor, Professors conduct original research and commonly teach undergraduate, professional course