The HP 1020 is a Laserjet, and the other one is an Inkjet.
It's not that you can't print on fabric with a Laser printer, but the methods and preparation are different because of the way the ink (or toner) is transferred to the paper/fabric/whatever it is you're printing on.
If you Google "fabric printing laser printer" (or inkjet), you'll see the different recommendations and procedures. Also look for memory quilts as those sites will also have tips.
Here's one:
http://www.brighthub.com/computing/h...les/58811.aspx
There are many sources - try to pick more recent ones as the articles written in 1998 ;-) might not be current enough. There are better solutions and techniques currently available. If you do a little legwork, you'll see all the possibilities.