If I play some soft music (vocal or instrumental) with the volume turned up . . . it doesn’t sound anything like loud music. And if I play some loud music with the volume turned down, it doesn’t sound like soft music. Why is that?
Well, for one on most instrument (or vocals for that matter) when you get loud the sound tends to “spread” which doesn’t happen when you digitally enhance it (i.e. the speakers on your computer). In addition, dynamics have a kind of “energy” attached to them. It’s a little hard to describe, but trust me I’ve heard enough long diatribes from my band teacher (well, former band teacher since I graduated I guess) about how we’re not doing it wrong and through first hand experience putting emotion behind the dynamics makes the music just sound different
Distortion may be a factor. As the record industry for absolutely no reason continues to raise the recording volume on CDs, they lose data as the sound wave gets clipped because it doesn’t have enough room to properly record the dynamic sound level. They’re destroying music for no benefit.
It’s about the characteristics of the instruments. To put it simply, if you hit, scrape or blow something hard, it vibrates not just more, but in different ways to hitting/scraping/blowing it gently.
Additionally, with some of the more versatile instruments, say the violin 
, it’s possible to give the perception of dynamic changes without a change in actual volume. The sound can be altered through varying the combination of bow speed and weight, or by varying the vibrato, while keeping the decibel level steady.
GorillaMan is right of course.
I would add a couple of thoughts:
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Sound is energy - it is vibrating waves of air. The origin of the sound imparts a complex set of vibrations based on a huge variety of factors. That is why we can talk on the phone with someone and usually pretty accurately gauge their gender, their age, their health (do they have a cold?), their place of origin, etc. We can detect subtle changes in the vibrations that these different characteristics impart.
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Well, the original loudness at the point of the sounds origin is one of those charactistics. The original loudness or softness changes the original vibration pattern - one is simply not the exact same wave form, raised or lowered - the wave form itself is changed. Little things like the distortion that a louder sound can drive through speakers, inclusion of additional echoes because a loud sound sends out more waves which are more likely to bounce around, reinforcing some frequencies and canceling others. A loud sound in a lively room will generate far more natural reverb, interact more with objects in the room, etc. We can hear ALL of that, even if we can’t discern each contributing aspect separately.
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The way something is recorded can have a huge effect on how it sounds. Recordings over the past 20 years have become much more “loaded” - the mix is much louder and the range of dynamics in most pop recordings have become much narrower as more signal is shoved through…
For singers, piano vs. forte is more of an expression marking that a dynamic. Piano means give the impression of singing softly or quietly while still being heard over the orchestra (or piano) to the back of the hall. Inaudible is not expressive.
Really effective orchestration can give the impression of singing much more quietly than we really are - for instance, if there’s a huge, booming crescendo just before, and the singer comes in over total silence, that can be a stunning moment.
I don’t want to imply that singers ignore dynamics, just that we don’t take them to mean ‘80 decibels down to 30 decibels’. The average Joe or Jane ought to still be able to tell there’s something different in the new dynamic.
Turning to volume control doesn’t make staccato music legato or vice-versa. “Moonlight Serenade” by Glenn Miller will still be smoothly articulated, no matter how much you turn it up. The tempo won’t be affected, either.
Yes, but dynamic and articulation are not equal. You can have a very triumphant legato piece that’s blaring and expressive (some parts of the Jurassic Park theme fit this IIRC) or a sweet jumpy quiet staccato tune (Hedwig’s Song from the Harry Potter movies comes to mind). I suppose you’re right that that’s the feel of the piece, but it doesn’t explain why louder =/= forte since staccato also =/= forte (well, if anything marcato would be more forte, but you can have a somewhat marcato mysterious tune as well).
The OP offers an interesting question in a way that I haven’t thought of before.
I tell my students that dynamics is like Thanksgiving – it’s about the relatives. I section might be marked forte, but it means that it needs to be louder than what came before it, or your part needs to fit a little above another part. Just because your part says “forte” doesn’t mean that you play the loudest in the band. The melody still has to come through, after all.
This is important for instrumentalists as well. I often draw sweeping roller coasters on the marker board. I point out that it isn’t the height of the hills that is exciting – it is the difference between the peaks and the valleys that makes a roller coaster exciting. To make a passage sound forte, make the notes right before it softer.
Ha. In my classroom, too often louder also means faster. 