They are the same thing.

A bigger hydrogen bomb. The staged Teller-Ulam design has no practical or theoretical yield limit.

The bomb based on the design by Edward Teller and Stanilaw Ulam was first proposed in 1951, and tested in 1952. The first practical H-bomb (thermonuclear explosive) was built in 1954.

Teller and Ulam designed the hydrogen bomb for the United States.

Edward Teller was determined to build it and invented many unsuccessful designs. Stan Ulam, working on improved atomic bomb designs, showed Teller the radiation implosion technique. Teller recognized this as the missing feature to make the hydrogen bomb work; resulting in the Teller-Ulam design. This was successfully tested in 1952, shot Ivy Mike at 10 megatons yield. Teller had already left Los Alamos a few months before the test to start Livermore Labs, so he was not involved.