Hello nabiyari1 ,
the differences depends on the person who uses this terms :)
In general a variant is every difference to the given reference.
The term "polymorphism" and "mutation" are usually used in a clinical environment. "mutation" often means "this is the variant that causes (most likely) our clinical phenotype". "Polymorphism" often means: "This variant have a frequency over 1% in the population, so we don't think it causes the clinical phenotype."
But there's a problem with this definition. Even variants that are quite often can cause the clinical phenotype (thing of lactose intolerance). And we have lot variants we know nothing/not enough about whether they causes the clinical phenotype.
So whenever possible one should avoid the term "polymorphism" and "mutation". Instead just say "variant".
If possible try to classify them based on the ACMG Guidelines on "benign", "likely benign", "uncertain significance", "likely pathogenic" and "pathogenic".
Let me give it a try too :) -> : is_a
Mutation -> Variant Polymorphism -> Variant Mutation !<=> Polymorphism Variant is the most general term, it refers to any genetic difference (e.g. sequence difference)
The other two terms refer to type and origin of the variation with respect to a population.
A mutation is a 'spontaneous' variation caused e.g. by a simple error in duplication, cell-division, strand-break, radiation, toxins, etc. It does not need to exist in the population, ancestry, or even the population of all cells in the organism. It is inheritable, if it affects the germ-line, but not necessarily inherited.
A polymorphism is a variation that exists in or becomes fixated within a population, e.g. if it is neutral or benefical. Therefore, at least two genotypes exist wrt. to the given variation/locus for which a prevalence can be assigned.
All existing polymorphisms must have started (some time ago) as a heritable mutation, but not all mutations become a polymorphism.
The orthogonal axis of the definition of variation is what is actually affected: from a single nucleotide, insertions/deletions, to chromosome re-arrangements.