When you are calling SNPs (I don't know what you used, samtools, gatk?) you are giving some settings to filter some events (like dismiss low coverage snps, or low complexity regions), or you might use some post processing with vcf tools for example, which can also do some filtering.
Therefore, not everyone substitution type change is a SNP. If it doesn't pass the filters of default settings, or user defined settings it is not going to be present in your VCF file, which is as the name suggests Variant Call File. And the word VARIANT is of great importance.
To go even further, snp calling with samtools or anything else is just an inconsistent name to be precise. To call something a SNP (which is a polymoprhisms) it should be present in at least 1% of the population, that is a common SNP. More often what you are calling SNP with those tools is just an SNV - single nucleotide variation. So the tool with it's filter settings is actually assessing whether the given substitution event is a variant (true positive) or an error.
And now more to elaborate:
If there really is no variant but it is an error and variant calling software is not calling a snv, you have a TRUE NEGATIVE
If there is a variant, but software is not calling it, treating the substitution event as an error, you have a FALSE NEGATIVE
If there is no variant, but the software is calling a variant, you have a FALSE POSITIVE
If there is a variant, and software is calling this variant, you have a TRUE POSITIVE
The matter to tell more or less for sure that this is a true positive or something else you need to validate this SNV. Usually you can import reference set of SNPs (hapmap, 1000 genomes datasets, whatever - which are usually either backed with a lot of data and often with experimental data), and check if your event at this position is present in those data files. If it is, cool, if not, you might have a rare variant there, and you just need to do experiment to validate (or I might be wrong)
If I made a mistake in my explanation, somebody please correct me :)