Ron Rosenfeld wrote:

Also, my recollection (and I could be wrong here), is that during the times
I get a "maintain ....ft until established" clearance, it's for a precision
approach. For non-precision approaches, I've received a "maintain ...ft
until crossing xyz"


"Crossing" is to be used if they vector you to a non-published extension of an
approach course. "Established" is to be used if they vector you onto a
published segment of an approach. Precision or non-precision makes no
difference.

(Ref 711065P, 5-9-1, and all associated notes, and 5-9-4, and all associated
notes.)