Yep, have to agree with the others, you are wrong on this. "AT" does in fact refer specifically to the Amp Trip setting. And by the way, it can be used in referring to either an ELCB or a TMCB, there is no specific delineation in that regard.
And to elaborate a bit more, there is a valid reason to list both values. In a lot of cases there are overlaps in the trip ratings available. For instance, you may need a 250A breaker for something. That could be a 250AF/250AT, or it could be a 400AF/250AT. An engineer may specify a 400AF because he knows that someday, the load may increase to 300A. If a 400AF breaker was specified, only the trip unit or rating plug needs to be changed, or in the case of a basic TM CB, at least the space requirements stay the same and the bus connections don't need changing in the switchboard. Had he specified a 250AF/250AT, upgrading might be a lot more involved if not impossible on a full switchboard.