Cats and dogs have what we would call red-green color blindness. But they don't see only in grayscale.
Dogs and cats are dichromats (having two types of color receptors). (Neitz et al. 1989, Loop et al. 1979) Their cones allow them to distinguish between blue and yellow wavelengths, but less well between red and green wavelengths.
In cats, the two cone types have peak responses to wavelengths of 445-455 nm (deep blue) and 555 nm (greenish yellow). (Jacobs 1993, at p. 429)
In dogs, these receptors have peak responses to wavelengths of 429 nm (blue) and 555 nm (greenish yellow). (Neitz et al. 1989, Jacobs 1993 at p. 427)
Jacobs, G. H. (1993). The distribution and nature of colour vision among the mammals. Biological Reviews, 68(3), 413-471.
Loop, M. S., Bruce, L. L., & Petuchowski, S. (1979). Cat color vision: The effect of stimulus size, shape and viewing distance. Vision research, 19(5), 507-513.
Neitz, J., Geist, T., & Jacobs, G. H. (1989). Color vision in the dog. Vis Neurosci, 3(2), 119-125.