It depends on the food, really. Citrus is a big deal, but if it's processed or packaged in any way, they don't really care. I go over about once a week to get groceries, get my mail, send a letter to my husband. Jam is ok, strawberries aren't. Pets sometimes need proof of vaccinations. Here's the short list of food that I tend to get in the US just because of prices:
Tex-Mex style food is largely, and sadly, unavailable. Velveeta to make Queso is $16/lb. No joke. Dairy in general is much more expensive - Milk near me is pushing $5 a gallon. Tortillas, refried beans, etc are hideously expensive (yay $3/can!)
Meats are pretty much the same. We don't have Oscar Meyer, but we do have Schneider's, and it's pretty much the same stuff.
If you want unsweetened Iced Tea, you need to order a hot tea and a glass of ice. No joke - unsweetened iced tea, much less cold-brew tea bags - is unavailable everywhere I've ever looked in this country..
That being said, there are some things which are marked the same, but do not taste the same. Which baffles my husband, and makes cooking an adventure. Ranch dressing tastes different in Canada. We don't know why. At all. It just does.
We tend to have a smaller selection of products, as well. So we'll have the basic Campbell's soup, like chicken noodle, but not the wonky flavours.
I'm going to go ahead and assume that the study visa is all worked out, hopefully with the help of the school - That's the biggest concern, and you may get flagged "over" just in order to deal with that. (I'm Canadian - American (This is the first time I've ever actually said that - the paperwork came through on friday!), My husband's American, my dad's Canadian, my Mom's American, and border crossings are sometimes no problem, but before my paperwork came through, they were also sometimes quite the adventure.
Good luck, welcome to Canada, and if you've got any more questions, don't hesitate to PM!