Generally I’d say those terms are just kinda as they are, something organic or natural sounds like it has life, fleshed out, feels like it has soul basically.
I would differentiate organic from realistic though. This might be a strange one but I personally think you need something to sound organic to be realistic, but you can have something sound organic without being realistic. When I say realistic it basically means does it sound like it would irl, and that’s a combination of everything. Organic tends to carry combined traits like tonality, tonal density, and presentation mainly (sometimes timbre). Where I would say to achieve realism you need that + time domain like dynamics, spatial recreation, speed and separation, transients, etc. So you can have something sound organic, but it might not sound realistic. But I can’t say I’ve ever heard something sound realistic without also sounding organic.
This is from an overall perspective though, if I would use realistic in isolation then it’s self explanatory, if I were to say like presentation is realistic, it’s just as you would think it means
How I would use the term, no from an overall perspective, but some aspects could be considered realistic even if it isn’t overall realistic. Perhaps dynamics could be realistic but tonality isn’t, or timbre is realistic but spatial recreation isn’t. Realism to me is the absolute hardest thing for a system to achieve, and personally I’d say the mass majority fail at that overall. But that’s ok, something doesn’t have to be overall realistic to be good imo (and could carry some traits that are realistic, but not all aspects)