"how are mutations and polymorphisms similar and how are they different"

Differences: A mutation is defined as any change in a DNA sequence away from normal. This implies there is a normal allele that is prevalent in the population and that the mutation changes this to a rare and abnormal variant.
In contrast, a polymorphism is a DNA sequence variation that is common in the population. In this case no single allele is regarded as the standard sequence. Instead there are two or more equally acceptable alternatives. The arbitrary cut-off point between a mutation and a polymorphism is 1 per cent. That is, to be classed as a polymorphism, the least common allele must have a frequency of 1per cent or more in the population. If the frequency is lower that this, the allele is regarded as a mutation.