Coherent light must have the same phase as well as the same frequency. Monochromatic light only has to have the same frequency. A coherent source is always monochromatic but a monochromatic source may or may not be a coherent source.

Are monochromatic waves coherent?

If two waves are monochromatic (having the same wavelength) and are of the same phase, these two waves are defined as coherent waves. Sources generating such waves are known as coherent sources.

Can non monochromatic light be coherent?

There's some subtleties around the edges of this question, but the short answer is yes. Non-monochromatic light is made up of some combination (which might be coherent or incoherent) of light of a range of different frequencies.