Control one circuit from a separate circuit
First, if the controller is running from its own battery, then you can connect its ground and the 24 V ground together (or any one point on each one, but the grounds is usually what you'd connect).

Second, you don't need this device to have amplification on its own.  You need to get the signal from one circuit to the other, but the receiving circuit can amplify that as it needs to.

If you really need isolation, then a mechanical relay, solid state relay, or opto-coupler is what you want.  If you don't actually need isolation, and it sounds like this is the case, then have a digital signal control a transistor as usual.