One awards the overall mix of the film’s sound design. The other is for sound effects added in post-production.
The Academy Awards are extra-judicious in what they honor. There are plenty of proposed Oscars — including best stunt coordination, best ensemble cast (or best casting), and best voiceover performance — but they seem unlikely to ever materialize. At the very least, it’s safe to say the Oscars will never come close to handing out as many trophies as, say, the Grammys, which reward nominees in more than 80 categories.
Meanwhile, the Academy seems to like its current number of 24 categories (plus a dormant 25th category, Original Song Score, which hasn’t been awarded since 1985 — when it went to Prince for Purple Rain — due to a lack of nominees). The last new category to be added was Best Animated Feature, first awarded in 2002 (to Shrek).
So why are there two seemingly interchangeable awards for sound design? The answer to this perennial Oscar question is that Sound Mixing and Sound Editing, similar as they may, uh, sound, do actually recognize two completely different things.
The award for Sound Mixing used to be called Best Sound. It rewards the overall soundscape — or soundtrack — of a film. In short, everything you hear in a film must be mixed together and set to certain levels, in accordance with the director's specifications, and that job falls to the sound mixers.
That's why Interstellar's nomination in 2015 proved somewhat controversial; the film's dialogue was famously difficult to understand, due to the booming noise from other parts of the soundtrack. Similarly, La La Land’s nomination in 2017 was derided by some because the lyrics of some of its songs are muddy and hard to hear over the instrumentation. Theoretically, the sound designers should have and could have fixed that (unless the director specifically asked for such an effect).
Meanwhile, the Sound Editing category used to be called Sound Effects Editing, and that's a good clue as to what it's for. Many of the sounds you hear in a film must be created by technicians, and this prize goes to them. If a movie contains lots of explosions or gunfire whose sound had to be created or enhanced in post-production it’s likely to be nominated in this category, which is why it’s often won by war films — like 2018 nominee Dunkirk.