1. Jack must have been late for the school. He got up late.
2. Jack must have been late for school. He got up late.
-------------------------------------------
What is the difference between 'school' and 'the school' in the sentences?
Does #1 mean he was late 'for another school,' not 'for his school'?
Does #2 mean that he was late for his school?
No one would ever say #1.
When you write or say "the school," you are referring to a particular building or group of buildings. Steve is right; it does not mean the same as 2, and would not be used.
You are right about 2.
The difference between "school" and "the school" in these sentences is the specificity of the reference.
In sentence #1, "Jack must have been late for the school," the use of "the school" suggests a specific school that is known or mentioned before in the context. It could be referring to Jack's school, the school he attends regularly.
In sentence #2, "Jack must have been late for school," the use of just "school" implies a more general reference. It suggests that Jack was late for the concept of attending school in general, rather than a specific school.
Based on the information provided, it is not explicitly clear whether #1 means Jack was late for his own school or another school. The context is not provided, so it is open to interpretation.
However, in #2, it can be inferred that Jack was late for his own school since the article "the" is not used. Without the definite article, "the," it generally indicates a more general reference.
To accurately determine the intended meaning, further context or clarification is needed.