Similarity between Min-Conflicts and Coordinate Descent in CSPs?
Am I right to say that apart from this difference, min-conflicts and coordinate descent are essentially equivalent? 


In the same sense that A* and BFS are essentially equivalent except for the choice of which node to visit next, yes.


  If so why are classified differently?


There are some problems for which Min-Conflicts performs asymptotically faster (in the expected-time sense) than Coordinate Descent, and vice versa. Ditto, there are some problems where one (generally) converges and the other (generally) doesn't.