The answer given by leekaiinthesky and partially in the comments on the question give a good general picture. I also think that the variation within the respective species is way less than between the species. Keep in mind that also archaic humans like Neandertals fall outside of the variation of present-day humans when you do a genome-wide (nuclear genome and mt-chromosome) comparison (see Briggs et al. (2009) for the mt-genome, and Green et al. (2010) for the first draft nuclear genome and Prufer et al. (2014) for the high-quality genome. Looking at Meyer et al. (2012) you see that even Denisova genomes falls outside of Neandertal variation for whole genomes); this means that looking at phylogenetic trees of either nuclear or mt-genomes, the Neandertal always forms an outgroup, independent from what present-day human populations you are looking at. This is roughly quantified to 1% difference between humans and chimpanzees, 0.2% difference between present-day-humans and Neandertals and 0.1% difference within present-day humans. The latter two seem to be fairly close, but: there are no fixed differences between present-day human populations, and this will blur the differences in intra-present-day human populations compared to the differences of present-day humans and Neandertals or chimpanzees.
However, there is one aspect that has not been discussed here which I think is very important for your considerations: trans-species polymorphisms (TSP). In the first part of my answer I was careful to always pronounce that major differences can be observed genome-wide, but genomes have a mosaic structure. When you look at specific parts of the genome, i.e. genes or haplotypes, these major differences do not hold and TSP are a very interesting special case of that. TSP are basically just gene variants, i.e. alleles, that are shared between species. This means that individuals between species might have the same variant, but individuals from the respective same species might have other variants. In simple terms this can be seen as individuals between species are more closely related at a given gene locus than individuals within species. Shared polymorphisms between species can in principal be caused by three mechanisms: (i) Genetic admixture and introgression, (ii) molecular convergence and (iii) TSP by either incomplete lineage sorting or splits in the lineage of alleles that predates the split of the species and both alleles are maintained in both species [Těšický and Vinkler (2015)]. This figure from Těšický and Vinkler (2015) shows the three mechanisms (see the green genealogy for an incompletely sorted lineage and the red genealogy for a lineage with an early allele lineage split).
The first two are fairly unlikely in our case, even though there is some evidence that admixture between humans and chimpanzees happened after the initial lineages split [Patterson et al. (2006)]. Incomplete lineage sorting or early splits in the allele lineage, i.e. the TSP variants are identical by descent, can be seen as TSP in a narrow sense. And this type of TSP has been described between humans and chimpanzees especially for immune-related regions (see Azevedo et al. (2015) for a review) that are under long-term balancing selection. You can think of this as a selective pressure that is fairly constant in time, acting on different species over a wide geographical range, and triggering a similar selective response in the species involved. Given that, it makes sense that the candidate genes are immune-related as most likely that selective pressure is mediated by pathogens. Azevedo et al. (2015) also note that maintenance of TSP variants by balancing selection is most likely mediated by heterozygote advantage or frequency-dependent selection - both make sense in a pathogen co-evolution scenario. So far, the number of reported TSP loci is really low (really just below a dozen or so), and there might be two reasons for this that are not mutually exclusive: First and obvious, there might be very few TSP. Second, these loci are very, very difficult to detect (as you want to exclude loci that are identical-by-state due to e.g. recurrent mutation) and we might simply not yet have the tools and power to find most of them.
To draw a bottom-line and come back to your question, I would suggest that your inter-species genetic gap model needs a minor modification. Even though the general picture seems to fit, i.e. there is a significantly larger difference in variation between species than within species, there also is overlap in the far tails between chimpanzees and present-day humans. These overlapping variants are not identical-by-state, i.e. due to random effects or recurrent mutations, but are signatures of polymorphisms in the ancestral population of chimpanzees and humans that are still maintained independently in both the split lineages.