The motion detection logic in both cases is exactly the same, so there must be something about the image data from the D-Link that is different from the built-in camera. Does the D-Link picture appear dramatically different from the built-in camera (darker, brighter, lower contrast, etc.)? Does the D-Link configuration page give you any controls over the image, such as brightness or contrast? If so, please try changing those settings to see if they have any effect on the motion detection.
