The previous answer is correct on the distinction. To add the technical specifics:
Hotmail/Outlook has a username availability check that fires as an AJAX call during signup when you type in the field. That endpoint is directly queryable, but Microsoft rate-limits it at the IP level after roughly 10-15 requests. At bulk scale, you'd need per-request residential IP rotation just for the availability check phase before touching registration.
Gmail uses a similar lookup but Google's signup flow also runs JS fingerprinting and behavioral analysis on the page. A raw requests approach won't get clean results — you need a headless browser with proper rendering and user behavior simulation to even get consistent responses from the availability check.
Practically: the checker is the easy part. As the last reply said, the real wall is phone verification at registration. One carrier number per account, no way around it at scale. Most bulk email registration projects hit this limit and stall there, not at the username check.