Depending on what bank you bank with, you can either "pull" the money from bank B to bank A by setting up bank B as an external bank in bank A's online portal.

Or, You can "push" money from bank B to bank A by setting up bank A as an external bank in bank B's online portal. It is more favourable to push money than pull money since it takes 2 business days vs 4-5 business days for pulling.

Tangerine allows you to do any of that online, once you do, they will deposit two random deposits into the other bank to confirm that the account information is accurate.

TD bank use to allow you to add an external bank if you call in and provide them the info (I don't know if they still do)

CIBC does not allow you to push money from it to other banks, you can however pull money from CIBC to other banks.

P.S. all bank accounts have to be in the same person's name to do so, if you are transferring to someone's else account, this will not work and you will risk getting your account frozen.