In general terms, adaptation is live in order to accomodate change in the environment, while mutation is any change to the genetics of a living thing other than sexual recombination. read more
Mutations are essentially directionless, and random, but Natural Selection pics the best and follows them to the next outbreak of mutation, becoming adaptation. So Mutation is a cause of variation, and some variations persist as Adaptation. read more
Depending on the success it confers to the mutant (i.e. the individual carrying the mutation), it can be considered adaptive (mutant has more success than non-mutants), neutral (no difference between mutant vs non-mutant) or deleterious (mutant is less successful than non-mutant). read more
The difference between a mutation and an adaption is that adaptions are always bettering the organism. Mutations can be benign, harmful, or helpful to an organism. New species are started when a mutation occurs, and through natural selection, the species thrives. read more