Probably 'river bank' is the best general term. The other terms are more specific as to their location (eg levee is used mainly in the southern states of the US) and their structure (eg whether or not they are man-made or natural).

A river bank means almost any area immediately beside a river. Most river banks are not man-made, and may not be significantly higher than the usual water level. An embankment or levee would usually be significantly higher than the usual water level, and may also be higher than the surrounding floodplain.