Voltage should be identical, yes. Plugging more or less than the voltage a system is expecting into its Vss slot could potentially damage or destroy your devices.
‘mAh’ is basically a measurement of battery life; in this case, higher mAh is pretty strictly better, all else being equal. A 600mAh battery would last almost three times longer between charges than a 220mAh battery, provided it physically fit and there were no other factors affecting its discharge rate.
Most of the other specifications for your battery that you’ve given are in the realm of secondary engineering concerns. It’d be nice if you could try to match or exceed the end voltage of 2.75V, in case that’s important for a monitoring circuit inside the receiver, but that’s not a concern I’ve encountered before now. Elsewise you’ll want to match or exceed continuous discharge current capacity to ensure the battery can power what it needs to, and trust that whoever designed the circuit ensures the battery doesn’t swamp anything.