All launcher I know jettison stages composed of both tank and engines. I do understand that:
the jettison process is useful to get rid of dead weight
jettison engines allows the use of more suited engines (optimized for certain altitude, thrust optimized for certain mass corresponding to the launcher's mass at certain instant its fly)
But, carrying engines from launch that are started only at high altitude implies carrying weight that is not immediately useful. Thus a design where as few engines as possible are ignited during the flight may be more efficient. I found such a design on the R7 (all stages started on the launch pad, jettison lateral booster -tanks and engines- during flight) and the space shuttle where the main tank is jettisoned alone when empty and main engines are running from few seconds before launch to the orbit insertion.
My question is: Is the American space shuttle the only launcher where at least one of the staging process is composed of dropping tanks without dropping engines?
As far as I know, the shuttle is the only such orbital launcher. The only reason to consider discarding tanks but not engines is if you're recovering the engines, and there are very few reusable launchers.
Discardable fuel tanks are very common on military aircraft for extending range, of course.