I may be a little off base here, but the whole question of "engineer" vs. "Professional Engineer" is one more of a legal nature, based on professional and personal liability. Personally, I am a degreed and licensed Professional Engineer in the Province of Ontario. As a member, I am bound by a legislated code of ethical conduct, with regard for public safety being paramount. All designs or advice, stamped/signed/sealed or not, provided by a Professional Engineer (in most parts of North America) that has a negative impact can, and often does, result in either a civil or tort law case. Most states and provinces require a combination of work experience (attested and approved by surpervisors past and present), at least a large protion of which is performed under the supervision of a licensed Professional Engineer, a check on the personal character,and mandatory exams (content varies, depending on state/province/country). Transfer of licenses between regions is not always guaranteed, and may require further exams. Non-degreed engineers may also apply, but typically require more extensive examinations to test their knowledge of theory and mathematics, as well as more detailed experience and descriptions of how the experience relates to the overall "field" of engineering.
That said, there are many situations where an unlicensed engineer may still perform design work, the most common being when a licensed engineer assumes overall responsibility for the work (and they better have good liability insurance if they do not check the details before signing off on a design). Any person can design or manufacture an item; the question is who will sue them first and how much jail time they will serve if the end result is damage to property or the public.