In game terms, a half-orc is a character to whom the half-orc racial adjustments are a better representation than either the human racial adjustments or the orc racial adjustments. If two half-orcs get married and have three children, one of them might be a half-orc while another is considered a full orc and the last one is considered a full human; but even the human is likely to show some minor cosmetic features of their mixed ancestry.
I can't speak for the Realms, in particular, but one of the founding assumptions from earlier editions is that half-orcs are incredibly rare. There aren't enough of them to form a self-propagating race, because it's rare for humans to mate with orcs in the first place, so the chance that two half-orcs would ever come across each other (in a pseudo-Medieval European setting where teleportation magic is almost unknown) is not worth contemplating. Look at Middle-Earth as an inspiration, and consider how many half-elves there are.
Faerun isn't Middle-Earth, though. Faerun is a ludicrously high-magic setting, where travel is much easier than you might expect. Maybe there are places where human civilizations are immediately adjacent to orc civilizations, and they have a border with a substantial half-orc population.
