I had half siblings but we never used the term "half" when referring to each other. Our parents taught us not to as they felt there were negative connotations to it.
However, I don't think the word should matter - it's the feelings that count. We all loved each other very much though, of course, we had our childish squabbles and so forth.
As for SGC, I think it's possible to love them, but I get that some people don't. Nor do I think that matters as long as you (general GP/SGP) treat them equally. What's in your heart is for you alone to know.
Ethel, if you would spend more on your own GC, I trust it wouldn't be obvious, especially not to the kids. Or if you gave yours additional Christmas gifts, for example, it would be on a separate day, not when all were together. I don't think it's what I would do, but as long as the SC don't know, I don't see how it could hurt them.
Hapgran, it may help to think of your situation from your GC's standpoint - more love can't hurt! But even if you never fully get past those jealous feelings, as long as you don't act on them, I think you'll be ok. Best of luck!