Heathenism is typically when the Nordic/Germanic polytheists use to self-identify - though there's been a trend among some of the Celtic polytheists to lean towards that term as well. In either case, it's used pretty much exclusively by folks following the northern European pantheons - I'm not aware of any other groups using the term.
The reason they favor this is differentiation, really. A large number of people assume that "Pagan" equals "Wiccan" (or, at least, "near-Wiccan"), and it's easier to say "Heathen" than to say "Pagan-but-not-Wiccan". Some Heathens do not even consider themselves Pagan any more, due to the "Wiccan Assimilation" of the Pagan community - they feel that they have little in common with a vast majority of the Pagan community (on both religious and secular levels).
There's some minor differences between the groups that you listed - typically based on focus, specific Nordic culture, etc. As far as I know, all three of the groups that you listed are Nordic polytheists of one form or another.
Racism is an unfortunate stain on the history of the Norse faiths - the legacy of WW2, if you will. There are several organizations based on fighting that (such as Heathens Against Hate), and the racist strains of Heathenry are less common than they had been. Remediating Heathenry's reputation is going to be just as difficult and time-consuming, unfortunately.