That’s true in general, but in this case, I don’t think it’s true (which is what I meant). A restaurant does not = all the food in the restaurant, but I think that Am Yisrael does refer to all the people in Am Yisrael. If Hashem loves Am Yisrael, it is because He loves the people in Am Yisrael.
Part of the difference lies in the fact that Hashem’s loving something/someone is different than a human’s love which is based on subjectivity and whims. So a person can love a restaurant without loving each part of it. Hashem’s love is real and complete, so if He loves Am Yisrael, He loves each part of Am Yisrael. And Am Yisrael is the people of Am Yisrael. They are one and the same. You can’t separate the two.
So there are two differences: 1. A restaurant does not = all the food on the menu. 2. Hashem’s love is different than a person’s love.
At least that’s how I see it. But I would be interested in seeing what the mefarshim say, if I ever have a chance.