Alerts are a text message (sent from the number 66368) or email you will get letting you know when a purchase is made. You can set up alerts on all transactions or for specific amounts or merchants. After you set up an alert, you will only get a notification when a transaction is made within the selected criteria.
Controls are settings that allow your card to decline transactions that meet certain criteria. You can set up controls to decline transactions that are over certain monthly amounts, merchants, or out of the country. Keep in mind that the more controls you set up, the more declines you may see on valid transactions. If your transaction is declined because of a control you set up, you can always remove the control and try again.