> but when I use Mail.app to send an email, I am the one doing the emailing, not the Google SMTP server acting as a mail transfer agent (MTA)
You seem to be confusing the MSA (https://en.wikipedia.org/wiki/Mail_submission_agent) and the MTA. If today your MUA (Mail.app) tried to connect to the destination mail host via SMTP directly it would get rejected. Some early MUAs did actually do that, but today almost all email gets relayed via an MSA and one or more MTAs.
You seem to be confusing the MSA (https://en.wikipedia.org/wiki/Mail_submission_agent) and the MTA. If today your MUA (Mail.app) tried to connect to the destination mail host via SMTP directly it would get rejected. Some early MUAs did actually do that, but today almost all email gets relayed via an MSA and one or more MTAs.