Difference between fermentation and leavening?
Leavening is rising by any means, so baking soda and baking powder (chemical leaveners) both apply here, as does yeast (fermentation).

Chemical leaveners like baking soda and powder work by mixing an acid (varies, depending on the recipe) and base (usually baking soda in some form) to produce carbon dioxide gas.

Fermentation is the process of yeast converting sugars to carbon dioxide and alcohol.  In bread making, the carbon dioxide is the desired product.  In beer or wine making, the exact opposite.  In both cases (beer/wine and bread), other byproducts produced by the yeast add flavour and are highly desirable.

There are other types of fermentation by bacteria (such as those used in yogurt-making, pickles, or sauerkraut) that produce lactic acid; but those are somewhat outside of the scope of this answer (although lactic acid fermentation by bacteria is responsible for the taste of sourdough breads).

To specifically answer your question - yes, yeast breads undergo fermentation (which is also leavening).  Quick breads like banana bread use chemical leaveners, which are not fermentation.