Single nucleotide polymorphism (SNP) or genetic variation in general, by definition are relative to a reference sequence. When we talk about databases of SNP as in ("dbSNP—Database for Single Nucleotide Polymorphisms and Other Classes of Minor Genetic Variation", or "A map of human genome sequence variation containing 1.42 million single nucleotide polymorphisms" -- titles of well known research papers), what is the reference genome? Similarly for defining a "SNP Map/Profile" of a person (in medical genomics), what is the reference genome sequence? Is there a de facto reference, or is it context dependent? There is a sentence "Scientists are trying to identify all the different SNPs in the human genome" at http://www.cancer.gov/cancertopics/understandingcancer/geneticvariation/page36 - what is the reference genome here?
I don't see your point. If we take e.g. the definition from Wikipedia:
SNP "is a DNA sequence variation occurring when a Single Nucleotide ... in the genome ... differs between members of a biological species or paired chromosomes",
there is no place for reference genome. SNP is just a variable position with (commonly) two alternatives in individuals of the same species. In whole-genome sequencing projects some SNPs can be discovered (namely those which are in heterozygous state), but definitely not all.
One can investigate SNPs and/or use them as genetic markers irrespective of the availability of the reference genome. That's the way one does it for non-model organisms - e.g. utilizing RAD Seq: you discover SNPs simultaneously with genotyping.
dbSNP actually indexes itself against several reference genome builds including hg19. you can see this in the ssID records - we use the bulk downloads and you can see them there as well.
Any difference with respect to any two genome builds is really a variant. You can see this in the case of tri- and quad- allelic variants. There are cases where entire sequences lengths are added or removed compared to a reference genome build. These are called insert/delete variants, which can contain short or single nucleotide variants as well.
will try to fill this out a bit more later... quick response here.