Specificity, mostly. There is a difference. They're both bigots, but they're bigots in different (but equally unacceptable) ways. Typical establishment Republicans ultimately want to get along with neoliberals/centrists, and vice versa, because they're comfortable with the current status quo- which is, yes, incredibly bigoted and needs addressing. They're concerned with maintaining their own power first and foremost, hence their platitudes towards pretending to care about racism and agreeing to idolize the likes of, say, MLK (when their forebears LOATHED the man) who are in direct opposition to their goals. Alt-righters are not comfortable with the current status quo and hate anyone even marginally to the right of themselves and feel they are holding back whatever race, nation, or culture they are a part of. They find allies in MAYBE Tea Partiers, but they hate typical establishment Republicans almost as much as they hate liberals and leftists.
Basically, one group wants things to stay the same as it has since Reagan/Thatcher, which clearly doesn't work due to the fact that many are still marginalized. The other wants radical change, but to benefit themselves and only them and theirs. Everyone who is already marginalized and not in their in-group (say, white, straight men and those in their patriarchal family units) will simply be trampled on even more than usual, while elevating the useful idiots who fit their in-group to their cause and casting down those who allied with neoliberals and those who thought they'd be the "exceptions".
So yeah. There's a difference.
Also they hate being called alt-right even though THEY coined that term.
If I talk about the alt-right, I do mean the alt-right or at least the alt-right/tea-party coalition that helped enable Trump. But I mostly refer to all of the right AS the right and all Republicans as Republicans, because the specificity of alt right vs. tea party vs. establishment Republican, while useful some of the time, is not useful all of the time. They're all flavors of shit.
EDIT: It's also worth noting that Republicans only exist in America. Alt-right can be used to describe many parties or parts of parties the world over. If you're only concerned with America I can see why it may seem redundant. But I'm as concerned for the marginalized abroad as I am at home. If I speak of the alt-right it's the group that includes Jordan Peterson, Sargon of Akkad and uyoku dantai. They can't be Republicans as they aren't American.
www.history.com
