There is a difference.
NURBS or Non Uniform Rational B Splines, basically mathematical modeling... not that you have to know a lot of math. And there is no actual geometry being created with NURBS, while there is when you create Polygons.
Whereas Polygons create faces, and points and vertices. Maya (or other 3d software) then has to keep track of all that, and that generally creates larger files. And I think depending on how wide scale the project is, using polygons can make your scene lag. At least when I have large polycount the file gets a little hard to work in sometimes.
Nurbs are also smoother, so that CAN give you nicer looking models. I know some people prefer nurbs to create characters. However, you can make models just as smooth with Polygons, but that can require a very large amount of faces or triangles.
I definitely prefer modeling with Polygons. I find it much easier myself. And out of all of my teachers who were in the industry at the time, none of them ever used NURBS at their places of work. That isn't to say that you won't see it be used, but Polygons are used more often in professional settings. But I know people who have made some amazing things with NURBS too, so it does somewhat depend on your preference too.
CONVERTING: You can go to the top of any menu set I believe. (probably best to be under polygons or surfaces anyway) But then click on your object, and then on the menu "Modify" then "Convert" and then you can choose "NURBS to polygons" or "polygons to subdivisions". !!However!! It's not actually recommended to convert Polygons to NURBS, because it usually requires a lot of fixing up after the fact. And always when you use a menu option, it's a good idea to click on the option box beside the whatever option.
I hope that wasn't too confusing for you :S
And I hope that helped at least somewhat.
Either way, if you want my opinion, I say Polygons are much better... but that's just an opinion.
here's some more information if you want to look into greater detail:
http://en.wikipedia.org/wiki/NURBS
http://en.wikipedia.org/wiki/Polygonal_modeling
Or of course, there's always the Maya Help files... those things saved me a lot when I was in school for this.