I've always been taught that a modulation is strictly a change to another key. But I've seen some people use the term to refer to when a song stops using the primary tonic in any form. I.E. You have a song in C Major and you start emphasising G for a bit. But you don't change to G Major you just use the common notes between G and C. So you kind of imply G Major.
Is that a proper use of the term modulation?
Your intuition is correct; that would not be a proper example of modulation.
I like the definition given in The Complete Musician by Steven G. Laitz:
Modulations include a strong cadence in the new key, and the new key continues after the cadence. They give the feeling that a new key has usurped the home key (at least for the moment).
I think Laitz's requirement of a strong cadence in the new key is really important here. Otherwise, we're looking at what many music theorists call a tonicization:
Tonicizations usually occur within phrases. They do not disrupt the feeling of the home key; they do not have strong cadences in new keys, and they are fleeting.
Musical use of the term "modulation" is a bit different from that of signal processing. In the earliest usage around 800 or so, a "modulation" occurred when a chant (or secular song I'd guess) added the Bb to the key signature (or removed an existing Bb). (Bb was the only mode changing sign.) As time passed, this use of "modulation" was extended to key changes after tonal structures became more prevalent.
Presently (and in the foreseeable future), this definition seems likely to stay or be expanded.
In contrast, small changes around the "home" key are termed tonicizations. This usage is closer to that in signal processing (like frequency modulation and amplitude modulation in radio.)
To effect a modulation, one does need to indicate a strong sense of the new key. Schoenberg suggests that one should use notes from the new key that are not in the old key, particular those that have changed (like using F# when modulating from C to D).
