  We introduce an analogue for Lip-normed operator systems of the second
author's order-unit quantum Gromov-Hausdorff distance and prove that it is
equal to the first author's complete distance. This enables us to consolidate
the basic theory of what might be called operator Gromov-Hausdorff convergence.
In particular we establish a completeness theorem and deduce continuity in
quantum tori, Berezin-Toeplitz quantizations, and theta-deformations from work
of the second author. We show that approximability by Lip-normed matrix
algebras is equivalent to 1-exactness of the underlying operator space and, by
applying a result of Junge and Pisier, that for n greater than or equal to 7
the set of isometry classes of n-dimensional Lip-normed operator systems is
nonseparable. We also treat the question of generic complete order structure.
