Most colorblind people aren't dichromats, they're so-called anomalous trichromats. Basically, the genes coding opsins in your eyes have a number of functional sites that tune the spectral sensitivity. Those sites are tuned as far apart as they can be in color-normal humans. Anomalous trichromats usually have a genetic error that causes their opsins' sensitivity curves to overlap more, which manifests as reduced color sensitivity.

This occurs in other animals as well.