No, they are two different mushrooms, but share a common name, hence the muddling of identification. The "shrimp mushroom" is Russula xerampelina (and related species) and gets its name because it smells like shrimp. "Shrimp of the woods," which this article is about, gets its name from its texture similarity to shrimp. The Russula is a red or dark brown-capped gilled mushroom, so it is easy to differentiate from the lumpy, white shrimp of the woods. This naming situation is common, and one that happens a lot among mushroom species because popular names overlap. When people associate mushrooms with something else, i.e. shrimp or chicken or oysters, there becomes a huge space for jumbling of species. Because of this confusion, a lot of people insist on only using the scientific names because they are clearer and obviously indicate the exact species being referred to. This forager appreciates that sentiment, but finds it elitist because there are huge numbers of foragers currently and from generations past that didn't and don't have strong formal educations. Afterall, foraging was considered a thing for the poor, unfortunates who needed to forage for sustenance (in North America). It is extremely helpful to know the scientific names, but it should by no means be used as a gate to keep people out of foraging or identification. Instead, we work with what we have, which is often confusing, and try to find ways to improve through education but being careful not to be exclusionary. Now we know there are two mushrooms with shrimp in their name, two species that look vastly different, and so we can easily use physical characteristics to tell them apart.