An allele is an abstract concept that is not well defined at the molecular level. Consequently you will encounter people who use it to mean either the whole sequence or the specific base. Both cases are informal usage; I lean more towards the whole sequence of the gene, but you will hear both.
What is a gene
From a formal genetics point of view technically speaking a "gene" is an abstract concept defined as a unit of inheritance: something that obeys Mendel's laws. Alleles are opposing versions of these units.
For most practical purposes we treat genes as synonymous with stretches of DNA that code for a set of overlapping RNA transcripts of similar sequence and function (technically a locus). This is because generally these stretches of DNA are inherited together. Exactly how this stretch of DNA is determined is not well defined and varies from project to project. But technically speaking it is wrong to say that that stretch of DNA is the gene. Of course we all do it all the time because it is convenient.
In some ways, the concept of a gene, or at least its equivalence to a stretch of DNA, is an outdated out because we know that recombination can happen within any stretch of DNA, and thus what we refer to as a gene will not necessarily be inherited together.
A computer science analogy for a gene
A computer science analogy might be: A class is an abstract concept. In many languages, an instance of a class and all its members may reside at a particular location in memory, but we would not say that that location WAS the class.
The difference between two alleles is caused by changes to the base sequence of the DNA. But an "allele" is neither a version of the changed base itself, nor the locus we are saying is equivalent to the a gene, but the abstract gene itself: it is the B or the b in your punnet square.
Now all this isn't to say that your should never talk about alleles as being either the particular base, nor the whole gene sequence, but rather that different people will use both at different times - at the level of DNA, the concept of an allele is ill defined.