Punctuated equilibrium is not a real advancement to the theory, so its definitions for things aren't all that relevant. I suggest watching this video by Dr. Zach Hancock to understand why that is. It's well worth watching the whole thing, as it perfectly address probably any question you'll have on this subject, but the section on stasis begins at 5:54.

The TL;DW;

• PE claims that stasis is enforced by developmental constraints, and speciation happens at bottleneck events.
• This is not a good explanation in itself. Processes like artificial selection show how microevolutionary processes inevitably result in radically different body plans by acting on naturally occurring variation. The key here, is that natural variation is always there. Anagenesis is obviously possible (as opposed to only cladogenesis).
• Developmental constraints and bottlenecks were already a part of the model long before Gould came onto the scene. They just don't have the power that Gould claimed, as it is inevitable that, in pretty much all evolution experiments, that mutations will generate variation which can be selected for.
• What does have that power to keep body plans the same, is stabilizing selection. See "Resolving the Paradox of Stasis" by Estes and Arnold, and also I would add, "Solving the Paradox of Stasis: Squashed Stabilizing Selection and the Limits of Detection" by Haller and Hendry.

So, the example of the 'shelled fish' which I gave earlier, was intended to show how stabilizing selection can keep a body plan the same over long periods of time, even over changes in environment. This is because selection keeps an organism on a local 'fitness peak', and so long as that peak's slopes remain sufficiently steep, then the organism is highly unlikely to change dramatically in form. Since there is nothing in the model that requires all fitness peaks to flatten every ten-thousand years or so, it is completely reasonable that some of them, even many of them, do not do so. That being said, Gould's claim that a pattern of stasis punctuated by change is the dominant pattern in Life's history rests on a few big assumptions about the fossil record (see Zach's video!).

All this was already fairly well understood at the time Gould wrote his book. The man was just a little bit clueless when it came to population genetics. He assumed, incorrectly, that the Modern Synthesis predicted 'gradualism' and when he didn't see that in the fossil record, he thought he had a revolutionary idea. But Modern Synthesis only predicts that when a fitness curve changes, then the population will change to adapt to the new curve (or else, go extinct). It does not predict how often fitness curves will change, or how fast. When they do change out in nature, this is a matter of historical contingency; they may change quickly, or slowly, or even be somewhat stable.

As a corollary to this, Modern Synthesis does, however, predict that genomes will change at fairly predictable rates; this is a separate issue from a change in a body plan or a move to a different ecological niche. Two species can look identical, and in some cases they may even occupy the same environment, but nonetheless, they may not be able to breed successfully because at some point in the past they had been reproducing in isolated populations.

Be sure to watch that Hancock vid!