Yeah, HD generally means 1920x1080 or 1280x720, which are basically how many pixels are used. Both that and the bitrate affect quality - obviously HD allows for more detail than SD, but it's possible to have very high bitrate SD and very low bitrate HD such that the HD actually looks worse than SD. That's pretty uncommon though since it defeats the point of having HD in the first place, but it shows technically the resolution alone doesn't guarantee quality.
Some TV channels broadcast in HD, but use a low bitrate so things commonly turn in to a blurry mush of pixels, but they can still call it HD. It's one of those marketing tricks