They address different responsibilities, and your business may fall within both regimes.
FINTRAC's MSB framework deals with anti-money-laundering and counter-terrorist-financing obligations. Depending on the activities performed, these include registration, a compliance program, client identification, recordkeeping, and reporting. FINTRAC registration does not constitute a license or government endorsement. FINTRAC MSB requirements, FINTRAC registry explanation
The Bank of Canada supervises payment service providers under the Retail Payment Activities Act. Its framework addresses operational risk, incident response, and safeguarding end-user funds where applicable. Holding FINTRAC registration does not resolve those separate responsibilities. Bank of Canada supervisory framework
One important point is the geographic scope. You should not decide that RPAA is irrelevant simply because all your customers are overseas. The Bank's criteria include providers with a place of business in Canada, and its guidance treats Canadian incorporation as one way of meeting that condition. The payment functions and any exclusions still need to be assessed. Bank of Canada registration criteria
My starting point would be a list of the services your entity actually performs. Who maintains the payment account? Who holds funds? Who initiates, transmits, or executes the payment instruction? Which functions are provided by someone else?
Use those facts to assess each regime independently. That produces a much more useful answer than asking whether a “Canadian MSB license” covers everything. It also prevents you from discovering an additional registration and operating requirement after you have already committed to a launch date.