
Lawrence F. answered 06/01/19
PhD candidate with 3 years of university teaching experience
This is a great question and is still a subject of debate in paleoanthropology.The answer ultimately depends on how we define a species.
As you mention, humans and Neanderthals are morphologically distinct. Features like the occipital bun, midfacial prognathism, lack of a well-defined chin, and aspects of the teeth allow us to reliably distinguish a Neanderthal fossil from a modern human. Prior to the discovery of ancient DNA, bones and teeth were all we had to go off. Under one species concept, the phenetic species concept, we can assign Neanderthals they all resemble each other morphologically more than they do humans from any part of the world.
Advances in ancient DNA research complicate this view. Under another species concept, the biological species concept, a species is defined as any group of individuals that can produce viable offspring. Until recently, we could not infer interbreeding from the fossil record. The genomes of humans and Neanderthals can be distinguished, however there is evidence of Neanderthal genes in most non-African humans. This suggests that humans and Neanderthals did interbreed, though not very often. They would therefore be considered the same species under the biological species concept. Adherents to this view typically assign humans and Neanderthals to separate subspecies, Homo sapiens sapiens and Homo sapiens neanderthalensis, respectively.
Race is a tricky topic in anthropology. When we look at human biological variation, there is no single pattern of variation that divides humans into distinct "types" or races. What we typically think of as race relates to variation in skin color and some morphological characteristics, but these are just two aspects of human biology that happen to be visible. Some features like skin color are adaptive to environmental conditions like solar radiation, while others are just the product of random mutation over time. This does not make any group "more evolved" than another; we are just adapted in different ways. So, we would not consider Neanderthals a separate race within humans since we cannot even divide humans into biologically distinct "races".
I should add that while there is no biological basis for human race, the notion of race has very real social consequences. Despite having no valid biological basis, societies have still developed concepts of race based on external characteristics like skin color. As anthropologists, it is our responsibility to dispel misconceptions about biological race and the social inequity that comes with them.