I've seen some pretty bad definitions of allele.
All alleles are genes, but not all genes are alleles.
Alleles are slightly different genes that can make a gene pair. They can make a gene pair because they reside in the same location in the chromosomes.
Albino and the corresponding normal gene can make a gene pair. They are alleles. Pied and the corresponding normal gene can make a gene pair, so they are alleles. One albino gene and one pied gene cannot make a gene pair, so they are not alleles. The normal alternative to the albino gene and the normal alternative to the pied gene reside at different locations in the chromosomes. They cannot make a gene pair, so they are not alleles, either.
The mojave and lesser mutant genes can make a gene pair; they are alleles. The spider and pinstripe mutant genes cannot make a gene pair; they are not alleles.
Clear as mud?