New Bug:  As a tester when u Find any issues and report to bug tracking tool then you entered as a New.

Open Bug: As a developer when you find New bug from tester side and reproduce successfully then dveloper change the status New into Open.

New: If any bug found by tester during the testing phase then it is logged as a  New bug.

Open: if the New Bug rectify by the Developer and they agree with this New bug then developer logged as a Open otherwise they logged Closed.