“Damp” and “moist” are words with similar meaning.  They both describe things that contain a small amount of moisture—not so much moisture as to say something is “wet,” but nonetheless an amount that is tangible, an amount that we can physically feel. 

Although the two words are close in meaning, they are not exactly the same and tend to be used quite differently.  First of all, “damp” often describes a condition that is unpleasant or unwanted (“damp bedsheets,” “a damp basement.” “a damp hotel room”), whereas “moist” more often describes a pleasant or desired condition (“moist skin,” “moist cake,” “moist soil”).  This is not to say that there are no exceptions to these tendencies, but, in general, when dryness in a thing is something we want, then it is not good when it’s damp (“a damp carpet”).  When dryness in a thing is not what we want, then it’s good when it’s moist (“a moist cupcake”).

It’s also important to note that a “moist” thing is generally a little more saturated with liquid than something that is just “damp.”   Wiping something with a “moist” cloth would leave tiny droplets of water on it, whereas a “damp” cloth would leave no visible droplets.  Something that is “damp” is not completely dry; something that is “moist” is nearly, but not completely, wet.  

Another interesting difference is that we rarely, if ever, use “damp” to describe something we can eat.  You can say “moist cookies,” but you can’t say “damp cookies.”  Well, you can, but it’s a little hard to imagine why you would!  This is because we generally feel dampness of an object by touching the outside of it, and we’re generally not interested in how the outside of a cookie feels.  With cookies, we’re mostly interested in what’s inside.  Moreover, dampness is something we sense with the outside of our bodies.  It’s not something we sense with the inside of our mouths!

One last tendency to mention is that “damp” tends to be linked with coldness in our minds, whereas “moist” tends to be linked with warmth or a neutral temperature.  “Moist climate,” for example, would be linked with places that are warm and rainy, as in “the moist climate of the tropics.”  “Damp weather” is associated with places that get abundant rain along with cool temperatures. “Damp weather,” like many other things that are called “damp,” is often considered uncomfortable and something justifiable to complain about.  “Moist weather,” on the other hand, does not seem to be as common a cause for complaint—either that or it is not experienced as frequently by the majority of English speakers.  In fact, the combination tends to be used mainly in weather forecasting rather than in ordinary conversation.  Interestingly, when we complain about warm weather that has some degree of moisture, it is “humid weather” that gets the gripes.

The following are some of the most common word combinations for “moist” and “damp”:

MOIST:  moist cake, moist muffins, moist brownies, moist lips, moist air, moist towelettes, moist soil, moist skin, moist eyes

DAMP:  damp basement, damp cloth, damp laundry, damp cellar, damp weather, damp fur, damp hair, damp room, damp washcloth, damp sheets, damp mop