I know that there is monochromatic and duochromatic, but what is it called when you have more than two colors in a picture? Like if you had a picture made of only 4 colors?
There is a slight confusion here. A tone is not the same as a color.
You can have a print on white paper using only black ink. You can have in the image black, white, light gray, dark gray, etc. Several colors, achromatic colors but colors.
When you have 2 inks of different hues, you can have different colors, not only 2. If you have yellow and magenta inks, you can have different tones of yellow, orange, red, and magenta. You can have pink, pastel yellow, etc.
When you are using 3 inks you call it a tritone. But you can have 3 inks, CMY, and have a pretty much a full-color image, except of dark neutral colors.
When you have 4 probably you call that polychrome. But if the 4 inks are CMYK you have a full-color print, color separation or CMYK print.
Note that I am referring to print because of the term duotone is specific for print.
But you could have 4 colors in a painting, like a Piet Mondrian painting, well maybe 5 if you count the white, you have probably, just a colorful image?
Sometimes in painting, you can have a clear limited color palette.
But you probably will not call it monotone or duotone, probably monochromatic, or "limited palette"