"Laugh" can be a verb or a noun it is a sound or action made by one person. examples: The boy had a high pitched laugh. (noun) I laugh every time I see that show. (verb) "Laughter" is more associated with the action of many people examples: At the park, I heard the sound of laughter everywhere. The children's laughter was a joy to hear.

To laugh is a verb but can also be a noun. He gave a short laugh and then began to cry. Laughter is only a noun, meaning the sound or act of laughing.

From what I understand, "laugh" is used as a verb and "laughter" is the noun.