Engineers are required to be licensed by the states in which they perform design work. There are two licenses that might be held by a structural engineer. A structural engineering license is abbreviated S.E., and a civil engineering license is usually designated as a P.E. for professional engineer. Some states also refer to "Registered Professional Engineers," which is equivalent.
A P.E. has generally a Bachelors degree in Civil Engineering, four years of experience and has passed an 8 hour Fundamentals of Engineering exam and an 8 hour Professional Engineers exam.
At this time, approximately 14 states also issue S.E. licenses, but the requirements vary significantly. Some require that a separate P.E. license also be held. Some require additional experience of 2-4 years be demonstrated after passing the P.E. exam. The S.E. exam is in addition to the P.E. exam where both licenses are required, and varies from 16 to 20 hours of total exam time. Some states have restrictions on the type of work that can be performed by a P.E. and an S.E.
In short, an S.E. has is as much or more qualified than a P.E. to do structural engineering, but a P.E. might be sufficient for your project.