In "old times" you did deploy to remote repositories, even Central. But today, you "deploy" ONLY to your private repositories/MRM hosted ones, while to get something to Central you need publishing. Publishing is NOT anymore supported directly by Maven (and is NOT deploy, that is a lifecycle phase involved on each module, overlaid, publishing is very different today).

So "deploy" -> is lifecycle phase, usually involves m-deploy-p, happens per each module (while we do support "at end").
"publish" -> is what one needs to perform to get artifacts available from Central, involves calling (proprietary) APIs, zipping/packaging of all artifacts being published, performing validation, etc. In Maven 3 there is no "logically equivalent" place to perform it, hence it usually needs extra extensions like https://maveniverse.eu/docs/njord/

In Maven 4 there is a new lifecycle after:all that may serve as a hook, but still, handling (proprietary) API and zipping is not handled there either.