I am also a Canadian, born and raised in Southern Ontario, and living on the west coast with my husband for the last twenty years.
To me, "come over for dinner" means come over, short socialising session with a drink while dinner is made ready for presentation, a fairly leisurely time spent eating, followed by another socialising time, usually an hour or two. It's a specific invitation for a fairly formal home-cooked dinner. Tablecloths and wine are involved.
There are variations, of course. Once, after having done the "come over for dinner" thing the day before, for example, I found myself left with more food than I could possibly eat before it went bad. I had another friend who was interested in the particular style of cooking, so I asked him to come over the next day, to help me eat the leftovers. He did the thing that people are calling 'eat and run,' but I don't think - as he is a young bachelor - that he gets invited to non-family dinner meals very often. I was more amused than anything, and feeding him certainly did put a large dent in the leftovers!
I sew with a close friend on a particular weekday evening, and she knows that she is welcome to share dinner with me that evening if she wishes. It is extremely informal - she gets whatever I'm having that evening for myself, which might be nothing more than a can of tinned soup with buttered bread. Since we normally eat at completely different times (dinner to me is early - 5-6pm, while she eats at 9pm or later!) there are days when she doesn't share my dinner at all as she had eaten a late lunch, or will be planning dinner later at home. (My husband doesn't generally figure into normal meals, as he and I eat completely different foods, and he makes his own dinner. It sounds strange, I know, but it works for us.)
We have no ceremony when we do this, and she is welcome to wander around my kitchen to find what she needs if she decides she wants something later. So while it's an invitation for dinner, it's more like having a family member at home than a guest.