Who knew there was another kind?
There's natural fusion, which powers the stars.
Plasma-based fusion, which attempts to replicate natural fusion and is the only approach that has had significant funding for decades.
Cold fusion, which had been taboo for so long that only people on the margins of science studied it, except in France and Japan.
And now I'm hearing about laser-based solid fusion, which works as such: ultra dense hydrogen isotopes + lasers = huge amounts of energy + non-radioactive waste (helium, presumably). Worth the read.