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You’re not technically wrong, but even Postgres’ docs [0] use the term Primary Key.

Postgres primary key indexes are not primary indexes.

I know that, I’m saying that it’s a fairly pedantic argument when even their own docs use the term loosely.

"Primary Key" is the term in SQL standard. The url you linked is in "Part II: The SQL Language"

Primary keys are primary indexes are two mostly unrelated terms.