What is the difference between the dye-na-flow and the regular jacquard fabric paints?

Dye-na-flow is a very liquid paint. Not a dye. It has to be heat set. It acts like a dye but there is no chemical reaction like there would be with dye and fabric. Regular jacquard fabric paints are much thicker than dye-na-flow paints more of a pudding or custard consistency. Both give good color on cloth but because dye-na-flow is so liquid it flows on to the fabric much more easily but won't work as well for stamping, stencils or printing on cloth.

How well do these paints work on cotton?

I have great success with these on cotton. I usually use a fine brush. They will bleed into each other and they will spread if you do not have some type of resist. For a resist I have used wax, hot glue, white school glue, and even mod podge. I apply it with a fine tipped bottle. Air dry and then heat set with an iron. If I'm using a larger brush, I try to dab off/let it drip before applying directly to fabric. Also I have wetted the fabric to get a lighter/pastel tone. I hope some of this helps.