Are you talking wire transfers or ACH payments? ACH is typically a much slower method of transferring money (1-5 business days) though it is generally free to do so. ACH also carries all of the risks associated with checks save the risk of losing a piece of paper before you can deposit it.
Wire transfers can happen almost immediately but typically cost $20-40 for one, or sometimes both, parties involved.
Most banks allow you to transfer between accounts at the same bank for free, and faster than ACH transfers because they can settle it quickly when its internal.
They’re free to and from Fidelity accounts. I’d guess the same for Schwab accounts.