Other than fingernails or toenails, what have you cut or snipped with fingernail clippers? ~

Fishing line
candle wicks

nothing

Your wire example is a nail nipper, not a clipper.  Your tooth example is a nail clipper.  

nippers:
 

clippers (but straight for toenails):


I have used nippers to cut or strip wire.  I don't use clippers for anything, including nails.  They seem to require a skill that I never mastered.  I cut the nail too short every time I try to use clippers.  

"Hangnails"