It is confusing to learners. I don't think there is any rule that applies to these usages. Even worse, the uses don't seem to be guided by logic.

One can be at home or at a/the nursing home.

One can be at work or at the office.

One can be at college or at the university. (AmE)

One can be at McKinley Park or at a/the park.

One can be at school or at a/the school.

Student or Learner

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