You are mixing up the model of an ideal opamp with a real one.
If you use an ideal opamp, the voltagegain is infinite. Hence, in a circuit where the opamp's operating point is on the linear section of its i/o-Diagram, nothing is amplified.
With a real opamp, the differential voltage between its inputs is amplified by a factor of 100000 or more.
Considering an inverting configuration, there's a feedback from the output to the input, limiting the overall amplification of the circuit. But while on an ideal op amp the differential input voltage will drop to zero, the differential input voltage of a real opamp will just be very small, as it can be read and calculated from the opamp's datasheet.
So, in a inverting configuration the whole circuit amplifies the input voltage. The real opamp amplifies its differential input.
And I don't know, what you consider single mode. The ideal opamp gives a s*** on which input is grounded or connected to the ballon in the clouds. It just gives an infinite positive voltage on its output when it finds any positive differential voltage on its inputs, and vice versa.
For real opamps there are of course nifty things like CMMR, but I don't know if this relates to your question. Can you give a source for your "mode thing"?