What do you mean paper grades? Like weight/brightness?
You have your basic, crap 20lb/84 brightness copy paper. Cheapest stuff you can buy, runs $2-$3 a ream, $20 a case. It's flimsy, thin, and transparent. Sucks for color, and it's extremely dull.
Next up is multipurpose, usually 20lb/90 brightness. Meant to go in copiers/faxes/ink jets, same thin flimsy paper, just slightly brighter for more vibrant text/colors. A little better than copy paper but not by much.
Normal ink jet paper is usually 24lb/90+ brightness. Paper thickness is definetly thicker, feels a lot better in your hand and depending on the brand, the surface may be smoother. Colors don't bleed at all from my experience. Plain text looks a lot better, pictures/color stuff looks fantastic.
Premium ink jet papyer is usually 24lb/97+ brightness. The brightest I've seen is 110+, made by Kodak, runs about $8.99 a ream. After about 97 or so the difference in brightness is rather hard to differentiate. I'm currently using 97 (Georgia Pacific) and everyone who sees the stuff I print out on it (just an old Deskjet 812c) remarks at how great it looks on the ultra white paper, compared to the bland and kind of blah 84 brightness copy paper. AFAIK, only HP and Kodak make 100+ brightness paper - HP's highest brightness is 108 iirc.
I will say this - once you go to normal/premium, you will NEVER EVER go back to copy paper or even normal IJ paper. The difference in the two is night and day. I'll pay a premium if it means better quality paper. To me it's a significant difference.
Oh - you might see 28/32lb paper at the store - that's laser paper. Seems to work alright in an IJ from my experience but it's made for a laser for a specific reason, better to just use the IJ specific paper