mhendo has it correct. From the student’s perspective, I would wager that most undergraduates don’t know or care about how the hierarchy works. Generally the person in front of the room leading the class is considered by students to be a professor, even if he or she is a graduate student, lecturer, or adjunct/visiting assistant professor (teacher who is not on the tenure track). With the internet nowadays students can probably find out a college teacher’s rank, but even in grad school I regularly run into folks who don’t know who on our faculty is full, associate, assistant, or lecturer.
Young prodigy full profs are rare, and I would suspect they mostly reside in the sciences, a field where one is likely to have gone to undergrad and grad school straight through. In my field, education, like much of the applied social sciences, there is a premium based on “real world experience” so most of us have spent some time working in nonprofits, in schools, and so on. I have a friend who worked in policy after undergrad, so she’s in her early 30s with a doctorate… pretty young in my field.
As mhendo said, the probationary period is usually 4-7 years, so in my field, it would be rare to see a full prof much earlier than age 40, and I don’t think I’ve seen one at research-intensive university. (Might be possible at a small liberal arts college, I’m not sure.)
So the rankings at US universities go as follows:
Adjunct: usually someone in the field in practice, might teach a intro class or a specific skill that the teacher is familiar with.
Lecturer/Visiting Assistant Professor: essentially, someone who takes on the same responsibilities as a tenure-track professor, but without the research and publication responsibilities. However, these folks might aspire to tenure-track positions, so don’t assume that this group is composed of “accidental” academics.
Assistant Professor: usually a recent graduate holding a doctorate. Most APs are tenure track and have the 4-7 probationary period in which to earn promotion and/or tenure. I would say most schools offer tenure once you make it to Associate. My institution on tenures full professors, which is kind of unusual.
Associate Professor: has met the requirements for promotion and most likely has tenure.
Professor (or full professor): This person is acknowledged to be a high-flyer in the field. Research, service, and teaching is usually at a very high level. They’ve been at it for some time. It sounds analogous to the UK version, from your description. These folks will be deans and department heads.
Professor Emeritus: a prof who has retired, but still has a lifetime appointment at the institution. He or she may or may not teach, research, or publish. Sometimes they just have an office and can rail about the evils of the world using university letterhead. Some are incredibly productive, like my mentor, who is publishing 2-3 books a year in his early 80s.
Again, especially at big state schools like I attended for undergrad, I’d think most students simply refer to the teacher generically as “professor” regardless of rank (though I have noticed that if the person is not a 30ish White male, it’s often assumed that the teacher is a lecturer or graduate student). A teacher will usually start the course by introducing him or herself, and then you know if it you can call your prof “Bruce” or “Dr. Sloppypants.”