RGB565 is used to represent colours in 16 bits, rather than the 24bit (RGB888) web pages use to specify colours. To make full use of the 16 bits, red and blue are encoded in 5 bits and green in 6 bits. This is due to the human eyes capacity to see more shades of green.
All the other colour pickers I could find offered an RGB888 colour picker and then converted it to the nearest RGB565, however as RGB565 only has 0.39% (65k vs 16m) of the colours of RGB888 this results in many selections producing the same output.
The following colour picker only allows selections from the RGB565 colours: