There's no difference. The quality of the dye job is kept when the thread is woven to cloth, so no value is created or lost by dyeing thread relative to dyeing cloth. The option is mostly useful if you happen to have more of one than the other, or perhaps so that suturers don't use your theoretically-valuable dyed thread for stitches.
I know of no way to use cloth only of a certain color in a stockpile, except perhaps by use of burrows to limit your dyers to only have access to one color of dye so that only cloth of a certain color is ever available.
I guess that's a way but that would require a ridiculous amount of micromanagement. And all it would take to mess it up is just one dwarf bringing an undyed or a different color piece of cloth to that stockpile area to completely mess it up.
I guess the best way to do make sure all dwarves are wearing the color I want is:
1. Dump all produced clothes and dyes (except for the specific color I want) into magma
2. Produce a large amount of cloth make sure it doesn't get woven into clothes, bags, ropes etc.
3. Assign it all to a single stockpile and force your dyer to work there in a burrow until he falls unconscious.
4. Wove clothes out of what's left when he gives out the message "No undyed cloth available".
That seems to be the only way as far as I see.
On the bright side you can force military to wear that one specific color you want... Too bad you can't dye steel breastplates :p.