The difference is that one of those is not like the others. There really is no such thing as an unlicensed (medical) doctor, nurse, or lawyer. While most engineers are not licensed as such--and PEs don't even exist for many branches of engineering. Of course, they can't say they're PEs if they're not but there really isn't a default assumption, aside from perhaps in civil engineering, that an engineer asserting expertise in something is licensed.
Fair enough. I was talking US where PEs are fairly rare outside of civil engineering and other subsets of engineering that deal with regulatory bodies a lot.
Generally in the US engineer is used pretty loosely. Some states are stricter. But even those who are, like apparently Texas, my first-hand experience is that most people don't pay much attention.
