Vibrato is small, cyclical pitch modulation. The best example comes from the bowed strings, where the fingertip rocks, without actually slipping along the string, minutely changing the point of contact and thus the pitch. Oboists don't actually produce vibrato but rather produce tremolo, a modulation in volume. There can be an incidental but virtually imperceptible pitch change.
Note that common bowed tremolo† is fundamentally different, in that the initial attack repeats; as with plucked string instruments as well. Because this doesn't occur with oboe, the term vibrato is used, regardless that it's technically incorrect.
( † A less common bowed tremolo is similar to oboe. The bow maintains its direction while the speed is modulated with hand motion. Though I've read of it and seen a demonstration, I don't know how it's notated or of any examples in the literature.)
A flutist can generate string-like tremolo with flutter-tonguing, oboe-like tremolo with breath control, and true vibrato (accompanied, I think, by subtle tone color changes).