Google Sheets List Cross-Check

I keep two separate Google Sheets. Sheet 1 holds my full list of names; Sheet 2 also contains those names but each row carries a status column. I need a reliable way to compare Sheet 1 against Sheet 2 and single out every person whose status in Sheet 2 is exactly “Registered Democrat”.

Whenever a match is detected, that row from Sheet 1 should be copied (or cut—whichever is easier to automate) to a brand-new sheet dedicated to these matches. If a name from Sheet 1 is not found with the “Registered Democrat” status in Sheet 2, it remains untouched where it is.

I’m fine with a straightforward Google Sheets formula (QUERY, FILTER, VLOOKUP, etc.) or an Apps Script if the logic is cleaner that way. What matters is that the solution runs inside the same spreadsheet file and I can refresh or re-run it whenever I update either list. A short note explaining how to trigger or edit it will be enough for hand-off.