Since Venus (śukra) can be seen just before sunrise or just after sunset as a bright morning or evening star, it is possible that a specific term for Venus has merged with the generic term for star. At twilight, it seems Venus is up to 15 times brighter than the brightest star, Sirius.
Based on the semantics of śukla/śukra 'bright', 'white', 'bright star', and the Tamil semantics as pointed out by Palaniappan, I now believe that DEDR was wrong to include the meanings of star in the same entry [DEDR 2646], along with the meanings of spot, speck, dot, water-drop.
Does Sanskrit śukla/śukra 'bright' have any Indo-European (or Indo-Iranian) cognates?