The dietitian says, "This is the school cafeteria."

What does the school cafeterian mean?
1. This is the (only) school cafeterian of our school.
2. This is the specific school cafeterian of our school.
[What does "This is the school cafeteria." mean?]

I'm the school nurse. I take care of sick students.
Why is 'the ' used before 'school nurse'? Can't we use 'a' instead of 'the'?
3. I'm the (only) school nurse of our school.
4. I'm the specific school nurse of our school.
5. I'm a school nurse.
6. I'm the school nurse.
[What does 'I'm the school nurse' mean? What is the difference between #5 and #6?]

Here are many examples of what "school cafeteria" means:

https://www.google.com/search?q=define+%22school+cafeteria%22&oq=define+%22school+cafeteria%22&aqs=chrome..69i57.9235j0j7&sourceid=chrome&ie=UTF-8

#1 means this is the only place where students and teachers can buy their lunches at school. I'd rephrase that sentence a bit, though. ~~> This is the cafeteria in our school. (no repetition!)
#2 is wordy and awkward. The best sentence of all these is this. ~~> "This is the school cafeteria."

Rephrased --
3. I'm the school nurse at our school.
4. I'm the nurse at our school.
5. (fine as it is; could work at any school, but hasn't indicated which one)
6. (fine as it is; works at THIS school -- whichever school is being referred to)

The school nurse is the qualified nurse who works at a school. In the schools around here, each school has a qualified nurse on campus, plus other people who assist her or him. The assistants usually don't have specific degrees or titles. The larger schools have more than one or two assistants.

The sentence "This is the school cafeteria" means that the place being referred to is the designated cafeteria for the school. It implies that there might be other cafeterias in different locations, but this one is specifically for the school being mentioned.

As for the usage of "the" before "school nurse," it depends on the context. If there is only one school nurse in the school being talked about, then saying "I'm the school nurse" indicates that the speaker is the one and only school nurse in that particular school (#3 and #4).

However, if there are multiple school nurses in the school, saying "I'm a school nurse" (#5) would imply that the speaker is one of the school nurses in that establishment.

If someone says "I'm the school nurse" (#6), without any further context, it suggests that they are referring to a specific school nurse that is known or relevant to the conversation. It could mean that they are the only school nurse in that particular school or they might be emphasizing their role as the most important or responsible school nurse in that context.