I have heard that going in between 2 parallel keys is just modal interchange and not a modulation because the tonic note is the same. Maybe if the change in key is short and only to add color to a piece that is clearly in a single key. But if there is a clear cadence in the new key or the passage in the new key is extended past simply adding color, I would argue that it is indeed a modulation. Especially if the parallel keys are major and minor(which is the most common set of parallel keys). For demonstration purposes I will use quotes and for actual examples, I will use classical music pieces that I know.
C, F, G, Am, C ... | C, Cm, F, G, Ab, C | Back to usual chord progression
That I would consider to be modal interchange between C major and C minor. No modulation because the cadences that exist here are all in C major. No cadences to C minor at all, just sudden shifts for the purpose of adding color. Now for an example of this in action:
The sudden C minor chord out of nowhere doesn't last long before it goes back to C major and there is no cadence to C minor so clearly, this is just modal interchange and the only real modulation going on there where the C minor chord appears is a modulation to E minor.
C, F, Am, G, C, ... usual progression in C major | C, Cm, Fm, Ab, Bdim7, G, Cm | Continues in C minor for long enough that C minor sounds tonicized
This I would definitely consider to be a true modulation to the parallel minor. It continues on in C minor as though C minor was the starting key all along. And there is a clear cadence in C minor. Both of these point towards a true key change, a true modulation, and not just C minor being used for musical color.
Now for an example of this happening:
There are multiple motions here from G to Cm in the Scherzo section. And then the C major comes out of nowhere the same way the C minor does. This, I would argue is parallel modulation because an entire section is in C minor, not just a few chords.
So is parallel modulation really a thing? Or is it just modal interchange, even if the parallel key gets tonicized?