I'm not sure where you are reading but both layman and scientists commonly use the word "human" to refer to the genus "homo". To look at just one example, Ian Tattersall called one of his books "Extinct Humans" and it is a look at the history of the genus homo:

https://www.amazon.com/Extinct-Humans-Ian-Tattersall/dp/0813...

There were 4 children, and one died. I have often wondered why the world's homo sapien population did not grow faster during the period 200,000 BC to 10,000 BC. In his book Extinct Humans, Ian Tattersall has argued that fully modern homo sapiens took shape around 200,000 BC and left Africa around 150,000 BC. http://www.amazon.com/Extinct-Humans-Ian-Tattersall/dp/08133...

The growth of the population was very slow. Someone suggested that at their peak there were 100 million bison worldwide, but it seems to have taken most of human history to catch up with the bison -- we seem to have hit that number only when we began agriculture. As late as the year 1300, the historian Fernand Braudel estimates a world wide population of only 500 million people. We became one of the most successful species in the history of the planet, so why wasn't there faster growth, for such a long time?

That question interests me, so it also interests me that a family, living alone, with fanatic Christian fundamentalist beliefs and no access to contraceptives, still only ends up having 3 surviving children -- not a whole lot in excess of the replacement rate.

Something similar to this must have been going on for many thousands of years.

"the actual make-up of cro-magnon brains"

There seems to be no agreement about what the word "cro-magnon" refers to. Possibly the phrase should be disused? I have frequently read that cro-magnon refers to the first homo sapiens who arrived in Europe. With that usage, "cro-magnon" is just a way of referring to us, a synonym for homo sapiens. But the phrase has other uses. Some writers continue to refer to "cro-magnon" as if it refers to some distinct species, different from us. But then, the question arises, which species are we talking about? Who is it related to? Why does it need a unique name?

As far as I know, the most exhaustive coverage of the various human species is in Ian Tattersall's book, Extinct Humans:

http://www.amazon.com/Extinct-Humans-Ian-Tattersall/dp/08133...

Tattersall is among those who refer to cro-magnon as homo sapiens, and therefore makes the phrase "cro-magnon" largely meaningless. One might say, with greater clarity, "Early homo sapiens in Europe."

Having said that, I should add, there is no doubt that Neanderthals (I'm using the spelling suggested by the Google Chrome auto-suggest, which may be out of date) were a distinct species, and that they had larger brain cases that homo sapiens. There is no evidence they were smarter than us. They never showed much advance toward abstract thought, which gives us reason to assume they were dumber than us, at least using traditional (habitual) notions of "smart" and "dumb".