I have had only dermabrasion one time about 5 years ago on a nasty scar on my face and let me just say dermabrasion and microdermabrasion may sound alike but they are as different as day and night. The main thing is that microdermabrasion peels off the top 10 to 15 microns (micro layers) and dermabrasion exfoliates a lot deeper. This makes it more invasive and a worse result imo.
Eric,
In answer to your question, a chemical peel uses an acid to cause peeling or exfoliation of the skin. It penetrates deeper into the tissue and may cause some downtime depending on the strength of the peel. A microdermabrasion is a mechanical exfoliation of the skin, it is non invasive and has no associated down time.