For an inverting opamp, is inverting the same thing as an 180 degree phase shift?

An inverting op-amp inverts the signal; it does not phase change the signal at the output by 180 degrees although, if the input waveform were a sinewave, then it would look like 180 degrees of phase shift.

How an opamp behaves depends on how you configure it in a circuit.

But the opamp is actually irrelevant to your actual question.

I think that your actual question is:

Is inverting a signal the same as phase shifting it by 180 degrees

What we mean by inverting a signal is multiplying the signal by -1, so +33mV becomes -33 mV and -0.5 V becomes +0.5 V.

A 180 degree phase shift is indeed related to time but since phase is also coupled to frequency we only tend to use phase when talking about a single frequency. The only signal that contains a single frequency is a sinewave. Now for a sinewave inverting it (multiply it by -1) or phase shifting it 180 degrees will result in the same signal.

So yes, for sinusoidal signals, inverting and phase shifting with 180 degrees is the same thing.

Also for periodic signals like square waves and sawtooth signals, which consist of a base frequency and harmonics, inverting and phase shifting with 180 degrees is the same thing. Then the phase is only related to the base (lowest) frequency.

For non-periodic signals (these do not have a base-frequency) this isn't the case.