The subject and the predicate (the verb and its modifiers) should make sense together; when they don’t, the error is known as faulty predication.

Tiffany, not her welfare, may not be safe.

The exemption, not the elderly, will be abolished.

An appositive is a noun that renames a nearby noun. When an appositive and the noun it renames are not logically equivalent, the error is known as faulty apposition. (See 48c.)

The tax accountant is a person, not a profession.