A tree worker with a hard hat is cutting down a branch.
A ballerina is climbing a tree.
There can be either a tree worker or a ballerina. One cannot be cutting down a branch while climbing a tree.
Sentence one is explaining that a tree worker is cutting a tree, and the second states a ballerina is climbing a tree. These are two different people doing two different actions.
A ballerina can not be climbing a tree while a tree worker is cutting down a branch.