Static rope is not designed to stretch under load. This is in contrast to dynamic rope which is designed with a certain degree of stretch. Static ropes have many applications including (but not limited to); abseiling, rappelling, fire rescue operations and caving. The low stretch properties of static ropes allow for a controlled, bounce free descent. As an example, abseiling ropes typically have a ~2% when under a standard body weight load. I think you can use either as your not bouncing around unlike a safety line for treestand harness which needs to absorb load when you fall.