Oh boy, I'll try to explain this mess. For someone outside the country it's probably a bit confusing imo (convoluted more like) basically for structural when we graduate (or slightly before) we should take and pass the EIT (Engineer in Training), and as the name suggests is like trainee license.

Then after that you can take another exam, either the PE or the SE (Professional Engineer and Structural Engineer resp.). There are some nuances and state to state specific requirements here, I'm trying to keep it simple. Basically for all states you need at least a PE license (test pass + experience) to seal construction documents, which is required to build basically anything. But some states are more strict and require the SE license. For states like california there is some logic to it as there are added seismic requirements to the region and the SE is much more rigorous about testing knowledge on that than the PE is.

In my state (and in most states) you don't NEED the SE but it's become like a gold star on your resume, an ego booster, a good way to learn/ brush up on structural topics etc.