a midi controller is an empty canvas wheras a synth is with its own internal sound engine. The source source for midi controller lies in the form of software instead, in the computer. When connecting midi controller to computer, the flow is such whatever thats being pressed or adjusted on the midi controller, it will send a command to the software instrument to control what its supposed to do, be it sounding a music note, triggering drum sound or adjustment of volume etc.
The control you mentioned, can be gotten through midi contoller as well. Other than just keys to talk midi, usually manufacturer also include a set of controllers in the form of faders, rotary encorder, buttons, pads, etc on the midi controller. With all these, you can "midi mapped" such control to the software instrument parameteres. Once mapped, whatever adjustment done on the midi controller itself, will be reflected as changes in parameters in the software instrument, which will change the sound of the software instrument.