I recently read a report that stated "We found 430 fixed substitutions […], with an additional 34 single nucleotide polymorphisms (SNPs) fixed within individual patients." What is the difference between both terms?
If you look into a certain population, you will find mutations (for example SNPs) in some ratio with the wild-type allele. When a mutation reaches fixation, it will be the only allele, reaching 100% penetrance in this population. See here for more information.
In the context given I would interpret it in the way that a total of 464 SNPs were found, 430 of these were in fixation (so can only be discovered when comparing them to another population) and 34 SNPs which haven't reached fixation and thus cannot be found in all members of the population.
Fixation is a process when one of the polymorphic alleles becomes fixed in the population gene pool due to genetic drift or natural selection and ceases to be polymorphic anymore. Therefore fixed substitution and SNP are two absolutely different concepts. So, the term “fixed single nucleotide polymorphism” seems to be oxymoron as it bears a contradiction. To calculate the real number of fixed substitutions at least one individual from another distant population or closely related species is needed.