Question about differential signals as input of an operational amplifier
The op amp doesn't know that the non-inverting input is tied to ground. The op amp only sees that the inverting input is a tiny bit above or below the voltage at the non-inverting input (assuming that we have negative feedback).

It's the negative feedback that forces the two inputs to be very close together.

So the op amp acts as a difference amplifier, amplifying the small difference in voltage between the two inputs. Because we have added negative feedback we have constrained the entire circuit to act as a linear amplifier with a gain determined by the resistor values.