Monsters in the new world are also called as demonic beasts. The reason is because they were born by demonic energy, causing their bodies to undergo mutation as their power go far beyond any ordinary beast. That's why their shape and structure is irregular without any specific patterns.
This demonic energy also let them to enhance their strength similar to ki or mana. They could also unleashed powerful energy attacks or spells with different force depending on how strong and what rank they were. Even the lower Bottom rank monsters, the weakest one among them have power comparable to a giant T-rex on earth. Perhaps as strong as the one Gohan fought on his childhood during his training with Piccolo.
Starting from the Lord rank, monsters are also called as Demon Lords. They possessed power vastly higher than the rank below them. Just a single one of them could easily cause a disaster and their attacks could annihilate a city in an instant. The demonic energy they possessed is also incomparable as the solid and thick purple energy aura will constantly clad their body once they entered battle state.
A Legendary rank monster is called as Demon Emperor. Other than having power that could defeat a thousand of Demon Lords, their characteristic is that the demonic purple aura will produced ominous black electricity similar to higher grade Super Saiyan. So far, their existence is extremely rare and scarce, hence they're legendary beings. Their realm of power have reached the Semi-Transcendent.