In the day-to-day operations and just the way they go about their business, there's not a whole lot of difference between a strata corporation and a co-op. Both have an elected board of directors that takes care of the day-to-day running of the co-op. It typically has a finance committee. It will have a maintenance committee, perhaps, and a gardening committee. These are just some of the more common committees that report to the board on those kinds of functions. If you look at it strictly as how you get done what you have to do every day, there's not much difference between the two.
A big difference comes at the level of ownership. In a condominium, what you own is the air space of your unit, right? That's yours; you have a separate mortgage that you pay to the bank or the credit union every month, and then you pay strata fees to look after the common property: the corridors, the elevators, that kind of thing.
In a co-op, you don't have a mortgage on your particular unit. The cooperative itself owns the building, and you have shares in the cooperative that entitle you to residence in one of the units of the co-op under its laws and regulations, so there's no individual ownership. That's true of an equity co-op as well as a non-profit, except that the equity co-op shares are obviously worth considerably more and they trade on the market.