The first nuclear bombs--called atomic bombs at the time--were nuclear weapons. They used fission and either enriched uranium or plutonium as the core material. They could produce an explosion ranging to about 25 to 30 Kilotons at most. The two used on Japan were between 15 and 20 kilotons.
Then the hydrogen bomb was invented. This used fusion of hydrogen for most of the energy produced. It worked by having a fission bomb, like above, at its core surrounded by layers of material rich in hydrogen that would then fusion when the bomb went off. These ranged up to 350 or so megatons. They were were a whole different animal thousands of times more powerful than the WW 2 nuclear bombs were.
The recent Beirut explosion was on the order of about one (1) kiloton. Imagine that amplified by say 2000 times in size. That's what a thermonuclear fusion bomb does. Both fission bombs and fusion bombs are nuclear bombs.
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