The maximum number of colors in a single GIF image is 256. GIF uses an indexed-color system: each pixel points to an entry in a palette rather than storing a full color value directly. With up to 8 bits available for each pixel’s color index, the palette can contain 2^8, or 256, entries.
Those palette colors are selected from a much larger 24-bit RGB color space, which contains millions of possible shades. GIF’s limit is therefore about the number of colors used by an image or frame, not the total number of colors the format can theoretically describe.
Animated GIFs can contain multiple frames, and each frame may have its own palette of up to 256 colors. Dithering can create the visual impression of additional shades by placing different palette colors next to one another. This is why GIF works especially well for logos, cartoons, diagrams, and simple illustrations, but is less suited to detailed photographic images.