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).