The full explanation is that the + and - terminals are a virtual short. Negative feedback will try to set the + and - terminals to the same voltage but no current flows between the two locations.
The amount of current (and the limitations of voltages) are set by the quality of the opamp. Better opamps have closer voltages at faster speeds at better currents.
Cheaper opamps will have a bit of error and diverge from the model. The delay can be largely modeled by capacitance over the + and - terminals (among other models of opamp errors)
But even a cheap opamp will keep the + and - sides within .05 Volts or so under typical circumstances.
With the infinite gain concept you can use a limit to calculate the behavior of any circuit.
This is only true for negative feedback cases but that's the most common case.
It is easier in most cases than infinite gain model IMO. Once you have voltage and current of that location figured out, everything else in the circuit is solvable by freshman level analysis.
When you calculate this with the feedbacks, it makes sense.