This is the result of nuclear fission, nuclear fusion or the two processes together.
No one has ever developed a "pure fusion" device. Just "pure fission" and "the two processes together".
atomic bombs, that use nuclear fission,
thermonuclear or hydrogen bombs, that use fusion.
These use "the two processes together". They are not "pure fusion".
The differences between nuclear and conventional weapons are, fundamentally, the effects that are produced by nuclear weapons, such as radiation, high temperatures and health and environmental problems.
Don't forget that nukes are vastly more powerful than conventional explosives.
If you set off a HUGE mountain of conventional explosives (far larger than anything that could ever fit on a weapon), and if you take the smallest possible nuke and then lower its yield even further by deliberate inefficiency, you might get the two explosions to equal each other in power. But that is taking things to unrealistic extremes.
For a more realistic comparison, the largest commonly-used conventional bombs have yields equal to about one half of a ton
of TNT. Most conventional bombs are smaller than that.
MOAB bombs, which are probably the largest possible conventional bomb, and are so large that it isn't practical to use them in most circumstances, have yields equal to 11 tons
The smallest possible nuclear weapons (small in size, weight and volume, without deliberately lowering their yield by making them inefficient) have yields equal to 10,000 tons
of TNT. Lower nuclear yields are achieved only by deliberately making a weapon inefficient.
The smallest strategic thermonuclear warheads that are deployed in today's arsenals have yields equal to 100,000 tons
of TNT. The US currently has 384 warheads deployed on our subs that have yields equal to 455,000
tons of TNT.
The US once designed, but never built or deployed, warheads for the Titan II missile that would have had yields equal to 35,000,000 tons
of TNT. Had we ever built this weapon, it could also have been carried in bomb form by our stealth bombers.