So I'm probably doing myself a disservice but according to a quick search on wikipedia...
An arrangement "is a musical adaptation of an existing compositition.... may include reharmonization, melodic paraphrasing, orchestration, or formal development."
A remix "(or reorchestration) is a piece of media which has been altered or contorted from it's original state by adding, removing, or changing pieces of the item."
Maybe it's the use of the term "orchestration" (or "reorchestration" for the latter definition) that's snagging me, but I feel they're very similar, perhaps all arrangements are remixes but not all remixes are arrangements?
I've always understood an arrangement is more or less going to be the same track. Same melodies, same chord progression, same pacing, essentially the same verses, chorus, etc... just played differently with minor changes. It's very easy to follow along and even sing to the arrangement (if lyrics existed in the original), without having to alter the lyrics much, if all. Essentially, one could play both the original and arrangement together and they'd generally mesh well. More often than not I'd see the term "arrangement" in of all places, VGMusic.
A remix on the other hand is a lot more elaborate from how I understood it. From completely altering the drums, to the chorus/verses, to maybe shifting lyrics around, completely changing or adding instruments/sounds that weren't there prior, but to a substantial amount that you may not be able to follow the song as easily. If one played an original piece and it's remix, it wouldn't necessarily mesh well. I remember in the early days of the internet when Napster/WinMX/LimeWire was common, it wasn't unusual to find "techno remix" versions of a song.
Is my understanding anywhere on point? In the above explanation, I'll often hear the "techno remixes" sometimes being wildly different from the source media. Different intros, drum beats, melodies, with hints of the original. Other times, it sounded mostly like the original song but with different instruments and drums, but melodies, lyrics, etc.. were all where they were - would that be more of a "techno arrangement"?