Are abscess and a boil treated the same way?

Yes... ...For all practical purposes. Both are localized infections, both need to be drained and, if necessary, treated with an antibiotic - although draining is often all that is needed.
Skin abscess. A boil is a skin abscess, a collection of pus localized deep in the skin. There are several different types of boils. Among them are the following: furuncle or carbuncle, cystic acne, hidradenitis suppurativa, and pilonidal cyst.If the abscess is small (less than 1 cm or less than ½ inch across), applying warm compresses to the area for about 30 minutes, four times daily may help.