Async BR: Asynchronous Business Rules are used when you want to perform additional actions after the main operation is complete without delaying the main operation. For example, you might want to send an email notification after a record is inserted without making the user wait for the email sending process.
After BR: "After Business Rules" (or "After Query Business Rules") in ServiceNow are executed after a record is queried from the database, but before the data is displayed to the user. They allow you to modify the data that is being displayed to the user. They are different from asynchronous execution as they are part of the process of fetching and displaying data to the user.
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