Lice are in the order Phthiraptera.

a change from a caterpillar to a butterfly

Sucking lice are a type of "lice" (or more correctly, louse). They are different from some other types in that they attach and suck blood from a single site whereas biting lice bite and get a blood meal quickly and then move on to bite at another spot.

Sucking insects are those insects who suck flowers and chewing iscts are those who just chew them

Lice (singular, louse) belong to a large order of parasitic wingless insects; order Phthiraptera. The headlouse - one of about 3,000 species of lice described so far - goes by the scientific name Pediculus humanus capitis.