Interac Online in Canada offers this, for Canadian merchants with Canadian customers. It’s basically cash over the internet. Makes sense you wouldn't have tried this if you weren’t :) [1]
Interac Online appears to have been deprecated by most major Canadian banks in favour of Visa Debit. My understanding is the Visa Debit cards issued by banks like TD and Scotia are dual-mode: transactions will be processed through the Interac network when possible, with the lower Interac fees applying, and through the Visa network otherwise.
I don't know if the merchant fees for Visa Debit are any different to using a Visa credit card.
Looks like its 50/50. Banque Nationale and BMO only issue vanilla Interac cards, and in RBCs case, you get two debit cards: an Interac and a virtual Visa Debit. To your point dual mode Interac/Visa Debit are not eligible for Interac Online.
When at a physical point of sale, a Visa Debit card is processed over Interac rails, and I believe Interac interchange prevails. At one point back in 2009 Visa was going to set up their own debit network in Canada, but as of 2010, my understanding is they gave up on the plan. The value add from the Visa Debit rails is for international online purchases, for phone purchases and for international point of sale purchases, neither of which are well supported by Interac-only cards.
[1] https://www.interac.ca/en/consumers/products/interac-debit/e...