For biochemistry, a “polymorphism” is one of multiple alternative forms within a protein or nucleic acid sequence. For genetics, a polymorphism refers to genetic variants within the population that allow evolution by natural selection.
A “mutation” is a change in nucleic acid sequence, such as in the sequence of a gene or its regulatory elements. Mutations originate from unrepaired DNA damage caused by replication errors and lesions from endogenous or exogenous mutagens as well as from insertion or deletion of DNA segments of DNA by mobile elements. Mutant proteins or nucleic acids that cause inherited diseases are considered mutations rather than polymorphisms even though they may exist in the population at significant levels – e.g. higher than the 1% level noted. A mutation may create a polymorphism in the population if the resulting variant form is transmitted to subsequent generations without causing major defects in biological functions.
On the other hand, a “mutation” could also be regarded as a physical event in a single individual/cell. A “polymorphism” is a population attribute. Unless they are lethal or somatic, mutations can give rise to polymorphism following increases in frequency due to either selection or genetic drift. In this case, one might refer to the "mutation" spreading or an individual "carrying a mutation" but this is just short-hand for "the mutant allele", i.e. "the genetic variant generated by the mutation" - it is not ACTUALLY a mutation unless it arose de novo since the previous generation. (In some cases, it might even be useful to consider polymorphisms within populations of somatic cells.)
When the new variant has some kind of affect, such as causing a human disease, it is obviously useful to use such short-hand but we should not confuse convenience/utility/convention with reality.
Souce: NovoPro 2018-03-12