AZW is the same thing as
MOBI, they are two different file extensions for the original mobipocket 7 format (and PRC is another).
AZW3 is the file extension for Kindle Format 8 (mobi8) and is the new-and-improved MOBI. It can more or less be described as an EPUB, but wrapped in the binary mobipocket database instead of a ZIP container.
AZW3 supports all the new goodies, like embedded fonts, dropcaps, SVG images, etc.
In other words, convert to AZW3 and you will be fine.