According to wikipedia [1] it is a single nucleotide (or rather a single base pair). But you obviously need more base pairs to identify which base pair you are looking at in the DNA. Presumably 50-150 base pairs is the length of DNA fragments required to be able to identify where in the genome it is.
> But you obviously need more base pairs to identify which base pair you are looking at in the DNA.
But that's not a SNP, then, that's a read that happens to contain a SNP.
Generally a SNP is addressed by giving the reference base, the mutated base, the chromosome, the base position in that chromosome, and the assembly used to align the read to that location. For example, a T->C mutation at chr2:25164877 using hg38.
Yes, you need to have the whole read to align to your genome assembly to detect the SNP. But before you do that, you don't know whether you have a SNP. And after you do that, the rest of the read is not useful if what you care about is the SNP.
[1]: https://en.wikipedia.org/wiki/Single-nucleotide_polymorphism