You can use a UNIQUE constraint if you want to give uniqueness to a column which is not primary key.
You can have more than one UNIQUE constraints in a table, where as there can be only one PRIMARY KEY in a table.
To modify a PRIMARY KEY constraint, you need to drop it and re-create.
Also, PRIMARY KEY column should be NOT NULL and UNIQUE constraints can be null.
If CLUSTERED or NONCLUSTERED is not specified for a PRIMARY constraint, the default value will be CLUSTERED.
If no clustered indexes are specified for UNIQUE constraint, NONCLUSTERED is set as default value.
Since a table can have only one clustered key, if you define a PRIMARY constraint and if it is not NONCLUSTERED, you can't specify a UNIQUE constraint as CLUSTERED.