Primary keys and composite unique keys(basic question)

             We have UUIDs in our tables which are primary keys. But in some cases

we also identify a composite unique key apart from the primary key.

My assumption is that there should be a unique key index created by us using the composite key. And when we fetch using this composite key instead of the primary key we have a performance boost due to the index.

Is this right ? Are there more details I should read to understand this better ? Please point. If I should use the query planner to look at the statistics I will.

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Thanks,

Mohan