Hi and welcome!
Yes, puppy coat is different from adult coat... the biggest difference being that it's easier!
You might as well start setting up your grooming "kit" now - there's no need for a specific "puppy brush", and you'll be using your grooming tools for the life of your little dog. Here's my basic kit:
- a pinbrush (we use the Madan brushes shown
here; the purple or pink are fine for an adult Sheltie)
- a slicker (
here's the kind I like)
- a
"greyhound" comb
- straight-edge scissors (you don't need anything fancy; Sally Beauty always has reasonably-priced scissors made just for hair)
- thinning shears (ditto above)
- a good spray-bottle to keep the coat moist while you work on it
You can go a very long way with just these six items (though you might want to throw in the
Illustrated Guide to Sheltie Grooming, too!).
OK, so, back to that puppy coat... take your water bottle and give the pup a gentle mist to get the coat a little damp. Then take your slicker and brush/fluff the whole coat up towards the head, in the opposite direction of growth. Then make sure that you slicker the silky hair behind the ears to ward off mats - oh, hit it with a little talcum powder while you're there, for additional anti-mat protection. That's all!

(NB. this is the
only time in your Sheltie's life when this approach to brushing will be acceptable [or effective]. Enjoy it while it lasts!) If you really want to get fancy, clean up the outline of the puppy's toes with your scissors, trim off the whiskers, and clean the edges of the ear-leather with the thinning shears.