In general the difference with a dye is it's is more like a ink which colors the wood. A stain is mixture of pigment suspended in a medium. There are some oil stains that contain dyes also.
I use Mohawk dyes so I'm not familiar with the ones you have listed. I would expect the Transtint, General Finishes and Briwax dyes to be about the same product with the exception that I've heard good reviews with the Transtint dye.