You can crosspost between Mastodon and Twitter in either direction using various third party sites.
When crossposting is switched on, it means when you post on Mastodon it will also be posted on Twitter (or vice versa).
This can be controversial if you're just mirroring your Twitter account to Mastodon without interacting on Mastodon at all. Some servers specifically ban such "zombie accounts".
However, if you're mainly active on Mastodon and mirroring it to Twitter there's no controversy at all.
There are many free open source crossposting services and sites including @crossposter at https://crossposter.masto.donte.com.br and @moaparty at https://moa.party.