A hue circle is sometimes divided into 12 sections and sometimes into 16. Neither is wrong: the two numbers come from two different theories of what color is, one built on how colors are made and one on how colors are seen.

12 sections
3 primaries
16 sections
4 primaries
Web-safe colors
top of the HSV cone

Left and middle: concentric hue wheels. Center: the primaries. Middle ring: half steps between them (6 or 8 sections). Outer ring: half steps again (12 or 16). The 12-section wheel starts from the RGB primaries, red, green and blue at 0, 120 and 240° of HSL hue. The 16-section wheel puts the four unique hues, red, yellow, green and blue, at the quarter points (roughly 0, 60, 150 and 240° of HSL hue; the exact values vary with the person and the display) and fills in between, so its steps are equal in angle but not in HSL hue.

Right: the web-safe colors that have a channel at full strength (91 of the 216, white at the center), seen from above the HSV cone: angle is hue, distance from the center is saturation. The web-safe levels give exactly six saturations (0, 20, 40, 60, 80 and 100%, the rings), and the hues fall every 12° around the outer ring (30 colors), so only some of them land on a wheel's spokes.

12 sections: physics and pigment mixing

The 12-section circle follows trichromacy: the eye has three kinds of cone (L, M and S), so reproducing a color takes three primaries. Mix light and you get the additive primaries red, green and blue. Mix pigments or inks and you get the subtractive cyan, magenta and yellow, or the painter's red, yellow and blue. Each primary gets the secondary mixed from its two neighbors, then the tertiaries between them: 3 + 3 + 6 = 12.

16 sections: human perception

The 16-section circle follows opponent-process theory (Hering). In the visual system color is carried on two opposing axes, red against green and blue against yellow. So people perceive four unique hues, red, yellow, green and blue, none of which looks like a mix of the others: there is no such thing as a reddish green or a bluish yellow. Pure yellow looks like it has no red or green in it, even though the light that produces it is a mixture of red and green.

Why they do not line up

The four unique hues are not evenly spaced in physical hue. On an RGB wheel, yellow, green and blue sit at angles that differ from where perception puts them, which is why equal steps on a mixing wheel do not look equal. Perceptual spaces such as CIELAB and OKLCH exist to correct for that.

Use the 12-section circle when the question is how to make a color or which colors go together by geometry, and the 16-section one when the question is how a color will look to a person.