2004:
Gore-Bush: Rural Southerners who supported Republicans on culture war issues
Bush-Kerry: Socially conservative Muslim-Americans who opposed the War in Iraq and who blamed Bush for increased religious discrimination
2008:
Kerry-McCain: Southern Hillary Clinton supporters who hated Barack Obama (i.e. PUMAs)
Bush-Obama: Conservative-leaning voters who were severely impacted by the 2008 Financial Recession
2012:
Obama-Romney: People dissatisfied with Obama's handling of the economy during his first term
McCain-Obama: Minorities who viewed Mitt Romney as out of touch with ordinary Americans
2016:
Obama-Trump: Protectionist working-class voters with overall moderate politics
Romney-Clinton: College-educated voters who viewed Trump as too incompetent to run a country
2020:
Clinton-Trump: Minorities who supported Republicans on culture war issues
Trump-Biden: Suburban voters who viewed Trump as too incompetent to run a country
2004:
Gore-Bush: Sounds about right although there are some moderate national security oriented voters who since became reliably D that fit in too.
Bush-Kerry: Moderate ancestral Reps who were turned off by Bush's perceived extreme conservatism and remain reliably Dem. Also some libertarian/isolationist types who would later become part of Trump's base. Granted Kerry didn't flip NH because of Black Muslims.
2008:
Kerry-McCain: Also some people who were uncomfortable with the idea of electing an African-American. Had Hillary Clinton been the main reason then a lot of them would've "came home" in 2016 which most of them didn't unless they began to hate her because she worked in the Obama admin. and those concerned about Obama's inexperience although the later group is a lot smaller.
Bush-Obama: Yes but I'd say close to half of them are now reliably Dem voters. The 2008 recession did a lot to discredit fiscal conservatism especially among those who aren't socially conservative.
2012:
Obama-Romney: Yes
McCain-Obama: Probably people who were in the second category of the above but thought Obama was doing a good job. Also a small but noticeable chunk of Mid Atlantic voters who approved of Obama's handling of Hurricane Sandy although most of these voters returned to the GOP.
2016:
Agreed with most of it although I think Trump's perceived extremism was more of an issue than incompetence.
2020:
I feel like the variables are more complex but it's still a good explanation.
