I recently was wondering if there was a name for sheaves which were locally constant on the open simplexes in a simplicial complex. After some googling I stumbled across simplicial sheaves. I am alright with the definition as the presheaves to simplicial sets, but now I wonder, is this the answer to my question?

Are simplicial sheaves related to the locally-constant-on-simplex etale sheaves of a simplicial complex? If not, does this concept have a different name? Are there interesting places this sort of thing appears?

What are the other interesting places where simplicial sheaves appear?

I know that this question is fairly general, but I hope you understand what I am asking.