Ubuntu and Mint are not the same thing, although Mint is based on Ubuntu and many things are similar / identical. The software packages are compatible too which is very good.
Mint is kind of like Ubuntu but with some additional plug-ins, codecs, other stuff added on top. And it looks much nicer (in my opinion).
So - you cannot "upgrade" from Ubuntu to Mint, but arguably if you started with ubuntu and installed all the extra stuff that Mint has on top of Ubuntu, and beautified it a lot, you would end up with something fairly similar.
Your best bet is to download and install mint.