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The Democratic Party is a big tent party. There is far left, center left, center, and center right. And of course the left-right spectrum is always going to be reductive. Joe Biden has been observed to track the center of the party as a whole over time, so he would be a center left politician.
As far as I can tell, they are 100% different. Guix uses Guile Scheme, NixOS uses the custom Nix language.