Interac is a private company acting as a payment processor just like MasterCard or Visa.

Each bank have an interface with Interac, and each terminal/cards that supports Interac as well.

This simplifies a transaction. The banks, terminal manufacturer and card manufacturers just need to make sure that their products are certified by Interac (or MasterCard or Visa) and they can make a transaction between them without interfacing with each banks, terminal and card manufacturers directly.

In exchange, the payment processor takes a cut. Usually it's a base fee + a percentage of the transaction. But each bank and merchants are free to negotiate these fees.

I think that all payment processors are private, but I could be wrong.

From memory, MasterCard and Visa are heavily based on EMV while Interac did their own thing first and then tried to somewhat converge towards EMV. So they have a funky specification. I think that Discover are based on EMV as well, but they do their own thing as well with a legacy payment processing (Diner's club or something like that)

Banks are risk averse, so trying to get into the payment processor market today would be extremely hard as all the major players already have an interface with the banks, and the terminal/card manufacturers want to ship as many unit as possible, so they pick popular payment processors.

Development and certification is expensive, so they try to do as less payment processor they can get away with.