Typically, one of these full-stack engineers works on both front-end and back-end. So on the web stack, typically they cover the two ends.
An engineer wouldn't be properly full-stack if the stack did not include both dev and ops. So being DevOps is clearly a part of it.
Some of these full-stack engineers take particular pride in including testing (as artifact creation) into their stack of skills. They can deal with testing so that they are not dependent on testers, and more importantly, so that they feel safer making changes throughout the stack that is getting too big to keep in mind at once.
The first place where the fullness of the stack starts really breaking is when we face the customer. Can a full-stack engineer expect to get all their requirements cleanly sliced, or should they also have capabilities on understanding, collecting and prioritizing the customer's explicit and implicit wishes? This is usually where a full-stack developer throws responsibility over to a complete product owner, who magically has the right answers. A Complete Product Owner is the customer-side match for the Full-Stack Developer.
And for me, the idea of being Full-Stack Developer breaks in another way too. The web stack isn't always the full stack. For me it most definitely is less than half of the stack. The system created with the web stack is just as dependent on the system created on C++/Python -mix than the other way around.
So frankly, my dear full-stackers. Your stack isn't full enough yet. Time to move towards polyglot. Onwards, to the unicorn state.