A facial is a series of treatments for the face while exfoliating with a scrub would be just one treatment. (Does that make sense? It sounded better in my head.)
When I get a facial they cleanse, steam, scrub, massage, and apply a mask to my skin. They also do extractions to remove blackhead, white heads, and safely pop pimples if you tell them its ok.
I've read that baking soda is a great scrub, but its very abrasive and that's why your skin feels so dry afterwards. Either mix it with something creamy/moisturizing when you scrub or slather your skin in moisture afterwards.