It seems to be quite difficult to find an answer to this. Are SNPs the same thing as alleles?
Alleles are variations of a same locus that codes for a protein (gene). These alleles can come in different forms, one of which is SNP. For example, sickle cell anemia arises from an allele of the beta-globin gene which has had a change from A to T. Meanwhile, for the ABO gene that determines your blood group, the O allele has a missing nucleotide (G) that leads to a frameshift in the gene and a loss of function. So alleles are caused by SNPs, but can also be due to deletions, additions, insertions and other genetic changes. Note that SNPs not always lead to new alleles. Sometimes they occur in non-coding areas and nothing happens.
SNPs do not need to be gene specific, but this was for simplicty.
@Artem added nicely to the answer, I'm quoting it here:
"Single Nucleotide Polymorphisms (SNPs) are Single Nucleotide Variants (SNVs) at a population allele frequency greater then 1%. Alleles are any variants of the same position of DNA, which includes SNVs, insertion/deletions, or structural variants and at any frequency." - @Artem