For applying inks, a brayer will give a smoother blending of colours than a sponge. I'd suggest looking at You Tube for Videos on sponging and brayering- it will give you a better idea of the difference, its easier to see it than explain it, lol. And brayering is not as difficult as it looks, its just practice, and the right technique.
This Lady has 2 excellent videos on how to brayer, I was hopeless until I watched hers. Its almost all down to how you hold the brayer.
The first two images are brayered, the tags sponged.