Difference between PRIMARY KEY index and UNIQUE-NOT NULL index

Hi all.
Maybe mine is a stupid question, but I'd like to know the answer if
possible.

In an inner join involving a 16M+ rows table and a 100+ rows table
performances got drastically improved by 100+ times by replacing a
UNIQUE-NOT NULL index with a PRIMARY KEY on the very same columns in
the very same order. The query has not been modified.

In the older case, thanks to the EXPLAIN command, I saw that the join
was causing a sort on the index elements, while the primary key was
not.

So ther's some difference for sure, but I'm missing it.
Any hint?

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