Is there any tangible difference between a unique clustered index and a clustered primary key?
One main difference is that the unique index can have a NULL value that is not allowed in the primary key. Clustered or not, this is the main difference between the practical implementation of a Primary Key versus a Unique Key.

Oh, and the fact that a table can have one PK and many UK :-).

These are both differences in INTENT not in PERFORMANCE.
Otherwise, I don't think there's any difference.
Behind any PK or UK the SQL Server builds an index (depending on the request, clustered or not) and the way it's used is transparent for the source is coming from.