Why does violation of PRIMARY KEY constraint retur

I am confused for a while since the Document point out:

When you create a PRIMARY KEY constraint, a unique clustered index on the column or columns is automatically created if a clustered index on the table does not already exist and you do not specify a unique nonclustered index. The primary key column cannot allow NULL values.

I have a table in SQL server with a PRIMARY KEY constraint. According to the above point,a unique clustered index on the column or columns is automatically created since i did't create any clustered in the table.

I learned 2601 Cannot insert duplicate key row in object '%.*ls' with unique index '%.*ls' from Database Engine Errors.

My question is that why SQL server return error code 2627 and not 2601 when I try to insert duplicate value in primary key column into my table which have a unique clustered index on primary key? Is it because 2627 has a higher priority than 2601 or what?

Can someone please give me some advice or help? Thanks.

A Primary Key, at least on SQL Server, is a type of Constraint. As a result when you create a Primary Key it is both a (unique) Index and a Constraint. Both error 2627 and 2601 have the same severity, so it appears that SQL Server will return the higher error code (as both a unique index and constraint were violated).

From testing, you'll only get the error 2601 is the column has a unique index that is violated, but does not have a constraint. Most likely, therefore, you'll see this on a conditional unique index.

Take the below examples:

USE Sandbox;
GO
--First sample table with primary key (Clustered)
CREATE TABLE dbo.TestTable1 (ID int PRIMARY KEY);
GO
--inserts fine
INSERT INTO dbo.TestTable1
VALUES(1);
GO
--Errors with code 2627
INSERT INTO dbo.TestTable1
VALUES(1);
GO
--Create second sample table, with unique Constraint
CREATE TABLE dbo.TestTable2(ID int,
                            CONSTRAINT U_ID UNIQUE(ID));
GO
--Inserts fine
INSERT INTO dbo.TestTable2
VALUES(1);
GO
--Errors with code 2627
INSERT INTO dbo.TestTable2
VALUES(1);
GO
--Create third sample table
CREATE TABLE dbo.TestTable3(ID int);
--Create unique index, without Constraint
CREATE UNIQUE INDEX ID_UX ON dbo.TestTable3(ID);
GO
--Inserts fine
INSERT INTO dbo.TestTable3
VALUES(1);
GO
--Errors with code 2601
INSERT INTO dbo.TestTable3
VALUES(1);
GO
--Clean up
DROP TABLE dbo.TestTable1
DROP TABLE dbo.TestTable2
DROP TABLE dbo.TestTable3

Note that only the last insert fails with error 2601; the other 2 fail with 2627.