On the team I'm on, here's our thoughts:
Update and Save are largely interchangeable. The only difference is, Save typically implies a page-change event, whereas Update usually implies that changes will be applied to what you can see, immediately (technologically speaking, usually accompanies an AJAX operation.)
For instance, an app my team is working on has a form where you can change the date that some event occurs on. We have both an Update secondary button - which uses an AJAX call to immediately push changes to the back-end - and a Save primary button - which returns you to the workflow. This screen is unique in our app, because it's used to manipulate date ranges; you can add days to a range, remove them, and even reorder days (they're accompanied by a short description, so the user knows what's what.)
We could make Update the primary action, and Save the secondary action, but we've noticed that when users were done with this page of our app, they tended to gravitate towards the Save button; when they still wanted to do other things and were making a safety save, it was Update.
Finally, it's worth noting that if you're only providing one option, it really doesn't matter too much - both give a good impression of what's happening. You could argue benefits for either one, so I suggest using what seems clearer to your testers. Also remember to consider color cues - a green button suggests progress in your workflow, so if your save causes another page to load, use that constructive color to your advantage!