Usually if it's called an "atom bomb" or "A-bomb" it's pure fission, and a nuclear bomb, thermonuclear bomb, or hydrogen bomb is fission-fusion-fission. A fission bomb compresses the hydrogen to cause it to fuse, and the extra energy and neutrons from the hydrogen fusion cause a whole lot of additional fission in the uranium tamper. For details look up the "Teller-Ulam" design, wikipedia has some good descriptions.