Overexposing means just that, giving more light than necessary to your exposure.
Similarly for underexposing.
Pushing means developing for longer. This is usually done in tandem with (and to compensate for) underexposing.
Pulling means developing for less time. Usually done in tandem with overexposing.
The confusion might be from the fact that many times people will say I "pushed X to Y" without mentioning the underxposure part which is usually implied. Then others will say "I pulled Z" and mean only the development part or only the overexposure part.
It's always better to be clear like "shot at X, devved at Y".
Pulling (i.e. overexposing *and* reducing development) colour negative film doesn't make much sense.
In B&W the effect of pulling is reducing contrast so you can capture a scene with high dynamic range without blown highlights or crushed shadows. As a secondary effect, you get less grain. The only sacrifice is speed, since you shoot at lower ISO when pulling.
In C-41 film, the main problem is colour casts when pulling (or pushing), and this is true for all colour processes. The 3+ layers that correspond to the primary colours and are calibrated with each other to give correct colour balance, don't behave identically under pushing or pulling, so the colour balance is affected. And it's not a simple, uniform colour cast, but it's different in highlights and shadows (also inbetween, but less noticeably so), which is a bitch to correct.
Now combine this major drawback with the fact that many C-41 films have wider dynamic range than B&W (primary point of pulling is to increase DR), so you see why pulling C-41 is a rare thing.
That said, you can overexpose a tad and be fine. It's a common thing to do, either to open up shadows a bit, or to be safe (from underexposure) if shooting at aperture priority with a not so sophisticated meter.