Yes, our description rather vague, but so is the setting in The Giver. We can't be sure when the story goes down, but since the memories of a distant past correspond to OUR world today, we conclude that it is, in fact, some time in the future.
Lowry has created in The Giver an entire world, unique from what we know but with certain similarities. There's enough to make it familiar to us, but elements that make us uncomfortable, too. For instance, Jonas has sexual urges just like we do (normal), but he has to take a pill to make his go away (weird). He has a family, with parents and a little sister (normal), but they're all selected by a committee to form a family unit (weird). This strange dichotomy is what makes The Giver so enticing.