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Anbu black ops are a special unit of shinobi. While Anbu is not technically one of the primary ninja ranks, most Anbu ninja were first jonin before they were recruited into the Anbu black ops. So in a sense, yes, they are generally more powerful than a regular jonin.
Jonin is the rank under Kage/Village head. Before jonin comes chunin.
There are actually quite a few, depending on what village you look at: In the Leaf, there are these: (Note: This is just an overview, not every single rank) Academy Student Genin Chuunin Special jonin Jonin Sannin Hokage (Kage)
Baki, a Jonin from Kazegakure, and the 4th Kazekage's most trusted Shinobi.
The ANBU you are talking about is Yugao Uzuki, the lover of Hayate Gekko, a leaf Jonin.