I think neanderthals and us (homo sapiens sapiens) had a common ancestor about 650,000 years ago. *I think*. then some of them moved to Eurasian and deveoped there into Neanderthals.
Homo Sapiens Sapiens developed an independent branch in Africa and then they (we) moved to Eurasia and around the world.
Two species can indeed interbreed; dogs and coyotes, donkeys and horses, domestic cats and some wild cats.
However I am unsure about our Neanderthal genes. I think I’ll wait until there is more proof and more research. Although, after we moved into Eurasia and joined what had become the Neanderthals, we co-existed for about 30,000 years.
Who knows what teenagers will get up to?
Rather than have our immediate predecessors living in Africa they want them to live in the Arabian peninsula (at least during periods when it seemed more verdent than at present).
They then develop in Arabia and a bunch move South down the African coast and end up ancestral to all the African types of people. Another bunch move East along the Indian coast and end up ancestral to all the Northern hemispheric types of people.
The Neanderthals simply got to Europe earlier, otherwise they split off from the crowd that moved to Arabia initially.
By the simplest definition, two populations are considered as belonging to the same species if they can breed and produce fertile offspring. By that definition, donkeys and horses are not the same species.
I'm not sure about the cats and wild cats. I had a cat that I suspected was a product of a domestic/wild breeding--whenever she would become emotional, her fur would raise up along her spine in a way that I have never seen in another cat. Her kittens (she managed one litter before we had her spayed) all looked like ordinary cats, though.