I am a mother of four which includes two singletons (who arrived first and second) and one set of twins. Perhaps because my twins are a girl/boy set, people haven't really had issues with seeing them as just "the twins". The one and only time that a gift was given to both of them was at their birthday party in which they received a slip-n-slide (and this one is another thing that is not a problem, along the same lines as other items mentioned that can be used by both--and the value of that is more than I think anyone [neighborhood friends, not family] would have spent on a single child). That said, if I ever had had a family member give just one item to both of them that is something that would just as likely have been given to one of my older two children, I would return the "gift" and say that just because they happened to be siblings born on the same day in the same year, they *are* separate individuals and deserve to be treated as such.
Now, when I initially was pregnant, long before knowing that I had twins, I had names picked out for a girl and a boy. They were not names like Robert/Roberta or other sets of practically the same name, just the masculine & feminine version, but distinct names. Even when I found out that there were twins and that one of them is a girl but we weren't able to find out before birth about the second baby, the second girl's name would sound like a reasonable choice for a sibling, but not overly 'matchy'. I did have people (strangers in stores type) who would, upon learning the names say "What kind of twin names are those? You should have named her [his name]a." (So, if I had named him Robert, they thought that I should have named her Roberta instead of Elizabeth.) I told even those people, though I probably never would cross paths again, that they are not a matched set of china, they are two separate people and besides, I really don't like the name Roberta. (True enough--the name that I actually did give my daughter is one that I had planned 'if I ever have a daughter' from the time I was 17 and saw the name in a movie's credits--and at that point, I was 35 and *not* going to give up that name just to slap a name that seems like "you're not what I really wanted, but you're an ok consolation prize". I have known twins with matching names (ironically enough, one set of names I have known sets of twins that were both male and another that are both female--Stacy and Tracy), but I couldn't ever do that to my own children.
As it happens, my daughter (only one in all four children) looks more like my middle son than her twin brother. While they still look very obviously like siblings, especially now, few people who don't know would guess them to be twins (she is not quite 5'3" and he is 5'10"--they're 12 now).
I do think one gift for "the twins" (especially the single t-shirt!) is different from other sorts of gifts that one doesn't really care for and is more akin to giving a book on the latest fad diet to an overweight person.