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Aren't they the same thing?

Not precisely. Most of the energy of a thermonuclear bomb comes from fission, the fusion reaction mostly serves as a booster for neutron flux, escalating the fission reaction further than in a pure fission weapon. Even more so when the enclosing capsule (The tamper) is made of U238 instead of lead, as the high neutron flux leads to fission in the tamper (The Tsar Bomb would have had a yield of 100MT instead of 50MT had it's tamper not been replaced by lead, an intentional restriction).

A proper hydrogen bomb would be purely fusion.

> A proper hydrogen bomb would be purely fusion.

But a fission device is used to get the fusion reaction going in all practical designs, I think.

The fine article describes the design of the US's actual hydrogen bombs as follows - I don't know if you'd count them as 'proper':

> So there are really three stages of nuclear reaction in such a bomb: the primary (fission), the secondary’s internal fuel (fusion), and the secondary’s casing (more fission).

The term "hydrogen bomb" has been used to describe thermonuclear bombs more or less since they were invented. Given that background, it makes no sense to me to insist that a "proper hydrogen bomb" would refer to a pure fusion design, especially since nobody has ever come anywhere close to figuring out how to build such a thing.

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