A band saw can be used to cut curves, even in thick lumber, such as in creating cabriole legs, rip lumber, and crosscut short pieces. The most common use for the band saw, however, is in cutting irregular shapes. 

What is the difference between a Jigsaw and a Bandsaw 

Bandsaws are used almost exclusively for re-sawing projects. Jigsaws are, by definition, hand power tools that cut with a reciprocating motion and are generally used to make various curved cuts on thinner material.