Three ways
Click the NBA button. It runs the side effect (email, invoice, calendar invite) AND advances the stage. This is the default.
Drag the card on the kanban. The card snaps to the new stage; only the stage changes (no side effect).
Use 'Move to a different stage' on the detail panel for explicit control. Useful for non-linear moves (e.g., re-opening a 'Lost' card to 'New').