Yes, there is a difference. A dominant gene will affect the phenotype of a heterozygous individual. For example, if C is curly hair (dominant) and c is straight hair (recessive), a person who is Cc will have curly hair, the dominant allele. A recessive gene requires that the person be homozygous recessive in order to exhibit the phenotype. So a person would have to be cc to have straight hair; being Cc is not enough.