Hydrogen bombs do exist. They‘re not really "mythical" at all, nor some sort of Alien Weapon. From what I can recall, they were developed fairly shortly after the first Atomic weapons were developed - only 5 years or so.
There are two types of "nukes", as it were. Fission and Fusion. The first type developed was Fission. It involved splitting atoms apart to create energy. The second type, commonly referred to as a "Hydrogen Bomb" uses Fusion. This process "fuses" atoms together to create the energy instead. Hydrogen bombs are a fair bit more powerful than their older brother, albeit more difficult to produce. Note that "fusion" is what powers the sun, as an example of its power.
As for this "sucking" effect, this occurs with both types of weapons. The shockwave spreads out from the blast, but creates an area of lower pressure behind it, thus causing the "sucking" effect, which is known to burst internal organs and shatter buildings.
For a great website depicting the weapons, their differences, and their effects,
click here