If the minimum temperature is higher than the dew point temperature no dew nor frost forms.  However if that minimum temperature is below 32°F with no frost, the conditions are sometimes referred to as "black frost," probably because that is the ensuing color of cold-sensitive vegetation exposed to such conditions.

If the minimum temperature is below the dew point, but above freezing, dew forms.

If the minimum temperature is below both the dew point and freezing, but the dew point is above freezing, then dew forms and later, as the temperature drops, freezes, resulting in frozen dew.

If the minimum temperature is below both the dew point and freezing and the dew point temperature is also below freezing, then frost forms.

Often, since both the condensation of dew and the deposition of frost are warming processes, the minimum temperature drops only slightly below the dew point.  Hence the evening dew point can be used as a guide to forecasting the next morning's minimum temperature.