Alleles in the traditional sense represent genetic variation in a population at a given locus. Usually this is related to a given phenotype or observable trait. They can refer to areas of the genome that may or may NOT be transcribed into RNA, whether or NOT that RNA gets translated into protein.
Alleles can refer to a single nucleotide difference (SNP), or an insertion/deletion of one more more bases (indels). Thus for a given SNP associated with heart disease, if 97% of the population has a T and the other 3 percent have an A at that locus, then the alleles are the A and T alleles for that SNP.
Note: the variation could be in a regulatory region of DNA and never get transcribed. But the phenotype associated would be varied expression of a transcribed region it regulates.
A transcript is merely an antisense strand of a region of DNA with U replacing T. Note there are many kinds of RNA transcripts, not all of which get translated to protein. The transcript always mirrors the DNA below. If the DNA has genetic variation, the transcript will reflect it.
In the last 10 years, with the discovery of epigenetics, we also have started thinking about a genetic locus where the variation is a modification of base or histone that the base binds to as DNA is compacted. So some now also include methylation of a CpG as an allele, where one person might have 40% of CpG at that location methylated, and another have 67%. This difference can explain a trait difference and thus also be referred to as an allele (high methylation vs. lower).
Last but not least, much genetic variation results in no discernible phenotypes. Sometimes both Alleles still result in the same base being encoded during translation for example.