I would say that mutation is most often used when the change creates a different phenotype in either the homozygous state or heterozygous state while a genetic variant has no measurable effect eg changes a redundant base while leaving the protein sequence unchanged  or is simply in an unimportant part of a gene so again has no biological effect but I expect that there is no clear cut difference as today's mutation may become tomorrow's variant and vice versa but I am sure that there are much better definitions out there

We have had this question before and it generated a lot of discussion and even some contentious disagreement.  Some folks raised the allele frequency as evidence of a variant rather than a mutant.  A variant might be 1% or more in the population.  Others used a functional definition for mutation as any DNA replication error.  I think there is no clear answer because the language is imprecise.  Mutations were originally defined as heritable changes in phenotype, long before we even knew what DNA was.  Variants typically arose as mutations and spread into the population.  In the end, they are both differences in the DNA sequence.  

A mutation is a heritable change in DNA sequence, NOT a change in phenotype.  All genetic variants are due to a mutation.

Appreciate all of the reply. I feel the border between the variant and mutations get more blurred with the evolution of science and knowledge. First variant has the idea of frequency that certain percentage of a population carrying the sequence, second, the variant is inherited from parents, born with the features. Not sure if variant has the idea that it should not change the coding sequence. However, the mutations have the overlapping features, it could be germ-line or acquired. In terms of carrying frequency, a good example is that in a country in Africa, most of the people there carrying a mutation in the gene coding their hemoglobin, which made the people insensitive to malaria. This case definitely reached the frequency in a local population but should be categorized as a mutation. Also, now a days, more and more mutations were found in promoter, in introns, or some other non-coding sequence. I feel we really need a clear definition to differentiate variant and mutations to avoid comparing orange to apple in future work.

With respect to N.S.Reddy note I would say that it seems incorrect completely that "mutation can termed as "polymorphism". Polymorphism is an existence of at least several forms (variants, alleles etc.). To my mind many of researchers make a mistake when they use term SNP describing in their studies effects only one variant of single nucleotide change.They rather describe single nucleotide variants (mutations) but not a polymorphism. One more time, it is a term describing an existence of many (poly-) forms (morph-). And it seems, we often perceive a mutation as a result of a change, and not the process of changes itself. So,some of the discussion points look like a result of a language imperfection. But not only ... 

Dear Dr. Zhang,

After reading some answers, it seems that it is more common to call mutation as "polymorphism" if the mutation frequency in a population is 1% or higher. But, possibly, more correctly to use terms as follows: "muation" - for single event;

"allele" - if mutation spreads in population and its frequency is 1% or more (Nobody names, for example, blue eyed humans as mutants). In some sense both (mutation and allele) are genetic variants.

As for term "polymorphism" - it describes an existense of two or more alleles of one gene, two or more phenes of one feature, two or more single nucleotide variants in a same position of DNA sequence (etc.).

To my mind it is incorrect to term mutation (even if its frequency more than 5 or 10%) as polymorphism. The existense of two forms (mutated and nonmutated) - that is polymorphism (dimorphism, more precisely).

Sorry, I added this answer, because of appearense new comment with the same mistake as earlier. Possibly authors use the same source of information.

in the report Standards and Guidelines for the Interpretation of Sequence Variants: A Joint Consensus Recommendation of the American College of Medical Genetics and Genomics and the Association for Molecular Pathology

Genet Med. 2015 May ; 17(5): 405–424. doi:10.1038/gim.2015.30.

the recommendation for changes with respect to human disorders gets round this issue by classifying all changes as Variants and then sub classifying them as one of 5 sub sections (1) pathogenic, (2) likely pathogenic, (3) uncertain significance, (4) likely benign, or (5) benign

which seems to be a good working classification

I think the ACMG's move away from the term mutation also carries a positive clinical consequence. I find patients respond much better to the term 'variant' than 'mutation' when discussing their DNA. This will becomes especially pertinent when we start discussing risk alleles and disease modifying genes in a clinical context.