SQL Server - AFTER UPDATE vs FOR UPDATE?

after update and for update are synonyms for the same behavior, namely that the trigger fires after the update operation.

They are identical.

From msdn page on CREATE TRIGGER:

AFTER is the default, if FOR is the only keyword specified.

SQL Server allows a lot of flexibility in syntax. All of the following are equivalent to each other as well:

• LEFT JOIN and LEFT OUTER JOIN
• INNER JOIN and JOIN
• INSERT ... and INSERT INTO ...
• Table AS alias and Table alias