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?
is also used in titles of lower ranks such as associate professor and assistant professor; this is particularly the case in the United States, where the word professor is sometimes used colloquially to refer to anyone in an academic post. This colloquial usage would be considered incorrect among most other academic communities. However, the unqualified title Professor designated with a capital letter usually refers to a full professor also in English language usage.
Professors often conduct original research and commonly teach undergraduate, professional and postgraduate courses in their fields of expertise.
Professor
Professor (commonly abbreviated as Prof.) is an academic rank at universities and other post-secondary education and research institutions in most countries. Literally, "professor" derives from Latin as a "person who professes" being usually an expert in arts or sciences, a teacher of the highest rank.
In most systems of academic ranks the word "Professor" only refers to the most senior academic position, sometimes informally known as "full professor". In some countries or institutions, the word "professor"