Both the terms nigger and negro come from the Spanish and Portuguese Negro which denotes "black". But today they have widely different connotations, the former is considered a horrible racial slur, while the latter was the prefered way to refer to a person of black ancestry or appearance until the 1960s–70s, was used by MLK in his "I have a dream" speech and is still used in the full name of the UNCF.
When did the terms go apart, and why does one of them have a strong racist connotation while the other doesn't?
Best Answer
Tone partly comes from origin, and partly from use.
If someone coins a word based on things already held in low regard, or start applying such a word to a group, then that word is going to start out with negative connotations. It could perhaps lose them, but the inverse is also true.
If someone coins a word that is not based on things held in low regard, it could still indicate a pointed distinction; that is, one bothers to point out that some people are X and treat those who are not X as "normal".
And with either of those, and even words coined with distinctly positive connotations, the word can acquire negative connotations through use.
And so it is with the words you mention. They are mostly used by racists, which makes them acquire the associations racists apply to them, which means that they are mostly used by racists.
Two particular influences were:
The abolitionists beginning to favour coloured. The more they avoided the terms n----r (and to a lesser extent, negro), the more that term was only used by racists, and hence the more often it would be associated with racist views, and hence the more non- or less-racist people would avoid it, and so on.
Objections to the extension of the word. In Britain it was sometimes used to refer to any foreign person who wasn't white. In the US the term "inside-out n----r" was applied to white people whose white privilege other white people wanted to remove or reduce (particularly those relatively new white immigrants to the US, particularly from mainly-Catholic countries, such as Ireland, Poland and Italy). Such people didn't object "well, technically that word applies to a different group to me", they objected to being associated with black people, who they too were mostly bigoted against, and that was indeed the intended insult. In using a word associated with black people as an insult to others, it increased the degree of insult not only to the target, but also to black people.
Some words flip, black (which outside of matters of skin tone has some negative connotations already) was once mostly used by racists, while coloured or negro were not. Negro started to be avoided because of its place in some phrases particularly associated with history (in particular house negro and field negro), and because it's got a madey-uppy othering quality that white does not. Meanwhile black was argued to be perfectly accurate (or at least as accurate as white is for white people) and not innately any more negative than white. As African-Americans started to favour black, the more racist people deliberately avoided it, and so the more so black lost its derogatory sense, and negro gained one, leading it to be further restricted only to racists, and so on.
There was also a lot of anthropological use of negroid, which was mostly pseudo-anthropological nonsense, and mostly racist. These days, while it retains some value in forensic and physical anthropology, the study by anthropologists of how different peoples define race has made any claim to objective distinctions between so-called "races" infeasible. See for example the American Anthropological Association Statement on "Race". The more that sort of anthropology was discredited, the more the term negroid and the related negro were associated with racist views, the more it would be avoided by all but racists. It hence also became a word that, especially when used by someone who isn't black themselves, doesn't mean "black person", but means "black person who, as such, I think less of". The shift is partly passive (racists just don't bother to avoid such words) and partly active (racists deliberately use words found offensive, because well racist people are the sort of scum that would do that). It is also particularly favoured by the worse racists, because they want to suggest their bigotry is based on some sort of scientific understanding.
We can find a similar shift in gay (originally coined as an insult based on the sense of gay of "sexually immoral") becoming the preferred term, while homosexual (originally coined as a neutral scientific term) is very often used by homophobes who want to portray their bigotry as neutral and objective.
Negress is particularly othering, in being a term for a black woman for which there is no comparable term (what's the word for a white woman?) and so combining sexual and racial discrimination in the very idea that we need treat black women as such a special case (and often, point of curiosity and target of sexual predation). As that became more conciously analysed with the growth of both the civil rights movement and the women's movement, and the (often fraught) intersection of the two (e.g. the Combahee River Collective), that led to both negress and negro being more disfavoured.
One possible response to all this is to think "well, this is all very arbitrary, if we just use all the words, they'll all stop being hurtful", as in e.g. Lenny Bruce's famous piece. In reality though, that's not very far removed from saying "gosh, it would be great if we'd all just stop being racist"; it's predicated on (a) bigotry being so rare among the more privileged group that they'd wash out the remaining pointedly bigoted uses and (b) bigotry being so rarely experienced by the less privileged group that such an experiment wouldn't be hurtful. If we lived in such a world, there'd be no need for such an exercise to begin with.