Gene:
Gene is a specific segment of DNA molecule which determines the inheritance and expression of a particular character.
It is the functional unit of heredity which carries information from one generation to the next.
Allele:
Two or more alternative forms of a gene are called alleles or allelomorphs. They occupy the same gene locus on homologous chromosomes but produce different effects on the phenotypes.
Example:
In pea, gene for producing height of plant may occur in two alternative forms: Tall(T) and Dwarf(t). Tall and Dwarf forms of gene are alleles of each other.