Apart from different colors, these two click boards are identical: both carry a 96x39px monochromatic passive matrix OLED display and a SSD1306 controller.
The SSD1306 controller allows horizontal and vertical scrolling, contrast control, inverse image display and more.
OLED W click and OLED B clicks can communicate with their target boards either through SPI or I2C interfaces. You switch between the two by resoldering three onboard jumpers.
The small displays are ideal for displaying lines of text or icons because they have low power consumption, yet have a sharp, high-contrast display.