Are these two OP-AMP circuits behaving different?
Yes they are behaving differently.


The first one is not inverting. The second one is inverting.

To be more accurate the output signal in the second one should look like  this (phase inverted; also the amplitude may be changed, depending on R1 || R2 and R4):


For most audio purposes or many other cases it doesn't matter if phase is inverted along the signal path or not.
And of course the first circuit includes a (quite) low pass filter consisting of R? (100kOhm) and  C? (100nF) at the output.

The second circuit doesn't. That's a big difference.