Wet, damp, dank, moist, humid are comparable when they mean covered or more or less soaked with liquid.
Wet may be used with no further implications or it may specifically imply saturation. Often, however, the term refers to a surface covered with liquid. But wet often means merely not dry, or not yet dry, especially when used in reference to something (as paint, ink, or glue) which has been applied to or used on a surface.
Damp differs from wet chiefly in implying a slight or moderate absorption or covering and often in connoting the presence of unpleasant or disagreeable wetness. However damp usually implies less wetness than is commonly suggested by the adjective wet .
Dank unequivocally applies to what is disagreeably, penetratingly or, from the point of view of health or comfort, dangerously, wet.
Moist often suggests little more than the absence of dryness or a not unpleasant dampness.
Humid is chiefly used to imply an oppressive degree of moisture in warm air.