Such creatures are called parasites.
Yes, bed bugs are parasites too.
Besides the lice that live on human beings, there are species that infest animals.
Bird Lice and Book Lice
Bird lice are not lice!
That is, they do not belong to the bug order.
They belong to a small order by themselves, but they are parasites like the lice.
The little white book lice that scurry away when we open an old book that has been standing on the back shelf, are not lice, either; they also belong to a little order of their own, and are constructed very differently from the true lice.