I wouldn't invoke a notion of "ground" when describing the operation of a component. That's some really a notion that comes out of looking at a circuit (in the sense of a circuit diagram), I would say. It might also confuse a beginner.
Otherwise I think your explanation is great. I can't claim to understand transistors super well, but your explanation touches on a key point for someone who is trying to understand the relationship between relays and transistors. Transistors cannot achieve the impossible--with 4 pins, you can achieve electrical isolation between the switcher and the switchee (and share a "ground" if you want to). A transistor cannot do that.
This might also be a high-level way to see why we need two "kinds" of transistors. Because suppose the electromagnet in the relay has some polarity, and only activates if current flows "north to south". Well, there are two possible choices of what side of the coil you tie to a pin on the switch, and what side of the coil you expose as the base/gate.
True ... ground in this instance could be a confusing word. I guess choosing an NPN transistor led me to choose that word but it's really more about the emitter being negative with respect to both the base and collector (kind of wordy). And the transistor becomes even more interesting because if the emitter becomes more positive than the other two connections, the base-emitter junction becomes a reverse-biased diode and blocks current flow completely.
Otherwise I think your explanation is great. I can't claim to understand transistors super well, but your explanation touches on a key point for someone who is trying to understand the relationship between relays and transistors. Transistors cannot achieve the impossible--with 4 pins, you can achieve electrical isolation between the switcher and the switchee (and share a "ground" if you want to). A transistor cannot do that.
This might also be a high-level way to see why we need two "kinds" of transistors. Because suppose the electromagnet in the relay has some polarity, and only activates if current flows "north to south". Well, there are two possible choices of what side of the coil you tie to a pin on the switch, and what side of the coil you expose as the base/gate.