If you want to switch from another UK bank to Monzo (or any UK bank to any other UK bank for that matter), you can use the CASS service (Current Account Switch Service) which has the banks involved switch your D/D’s from the old bank account to the new bank account. Salaries are not included in this switch though - you have to tell your employer yourself about the change. The Monzo ‘add salary’ is a feature which makes it easy to present your new Monzo bank account details to your employer to allow them to pay you using the new (Monzo) bank account - that’s it.
Re: ‘Salary Sorter’ (which works with ‘Get Paid Early’) - this is a Monzo feature which allows you to sort any income over £100 between your Monzo accounts, pots, and Joint Account connections in one ‘sort’. You can choose the amounts to send to multiple accounts/pots and initiate the move(s) with one tap. You can also save these ‘sorts’ so that future sorts are the same when the same income arrives. This feature is worth its weight in gold - salary arrives, tap on ‘sort’ - check amounts to be distributed are correct and tap to confirm - job done!
But Salary Sorter (in the Monzo sense) has nothing to do with receiving your salary into a Monzo account when moving from another bank to Monzo (via the CASS service)
Hope this helps! (BTW, I’m looking forward to claiming one salary early, this Friday instead of next Monday, and will be immediately almost-auto-sorting that salary between our Monzo accounts and pots)