What is the difference between Iascylla and Azir, Sovereign’s uses of “this battlefield”?

Iascylla’s delayed trigger refers to the battlefield that she held. Azir, Sovereign’s attack trigger refers to the battlefield where he is located.

The difference between these two is that Iascylla has a delayed trigger that references implicit information from her trigger condition: the battlefield where she held. Azir, Sovereign’s attack trigger does not reference information from his trigger condition, which purely checks for the event of Azir gaining the attacker designation for the first time each combat. Without that information being checked from the trigger condition, the “this battlefield” in Azir, Sovereign’s attack trigger will be checked when the triggered ability resolves. If it resolves and he is not located at a battlefield, any instructions related to that battlefield will be ignored; otherwise, the battlefield he is currently located at will be used.

Comparatively, when a triggered ability refers to information from its trigger condition, that information is checked when the ability triggers and not on resolution. In the case of Iascylla, her delayed trigger is linked with her hold effect, so the information from the trigger condition of the hold effect can be shared with the delayed trigger.

In future sets, they’ve moved to use more precise templating and wording for abilities like Iascylla’s.