This script proves things nicely:

CREATE TABLE #TestUpdateA

(ColA CHAR(1),

ColB INT)

GO

CREATE TABLE #TestUpdateB

(ColA CHAR(1),

ColB INT)

GO

INSERT #TestUpdateA (ColA, ColB)

VALUES ('A', 0)

INSERT #TestUpdateA (ColA, ColB)

VALUES ('B', 0)

INSERT #TestUpdateA (ColA, ColB)

VALUES ('C', 0)

GO

INSERT #TestUpdateB (ColA, ColB)

VALUES ('A', 1)

INSERT #TestUpdateB (ColA, ColB)

VALUES ('A', 2)

INSERT #TestUpdateB (ColA, ColB)

VALUES ('B', 1)

INSERT #TestUpdateB (ColA, ColB)

VALUES ('C', 1)

GO

UPDATE #TestUpdateA

SET #TestUpdateA.ColB = #TestUpdateB.ColB

FROM #TestUpdateA

JOIN #TestUpdateB ON #TestUpdateA.ColA = #TestUpdateB.ColA

GO

SELECT *

FROM #TestUpdateA

GO

TRUNCATE TABLE #TestUpdateB

GO

INSERT #TestUpdateB (ColA, ColB)

VALUES ('A', 2)

INSERT #TestUpdateB (ColA, ColB)

VALUES ('A', 1)

INSERT #TestUpdateB (ColA, ColB)

VALUES ('B', 1)

INSERT #TestUpdateB (ColA, ColB)

VALUES ('C', 1)

GO

UPDATE #TestUpdateA

SET #TestUpdateA.ColB = #TestUpdateB.ColB

FROM #TestUpdateA

JOIN #TestUpdateB ON #TestUpdateA.ColA = #TestUpdateB.ColA

GO

SELECT *

FROM #TestUpdateA

GO

DROP TABLE #TestUpdateA

DROP TABLE #TestUpdateB

GO