I guess it was exactly as you write - but instead of slightly earlier or later, the "lost" sounds are the high frequencies (a lot of hissing, clicking etc.) - the actual sound is mostly still there, but slightly "muffled" because it contains only the lower-frequency components.

With space not much of an issue anymore, FLAC is pretty much the default nowadays. And even though Opus and AAC and others have better encoding than old MP3, but I guess a 128 Kbps MP3 encoded in the original Fraunhofer l3enc (the best back then) and one encoded with LAME will be different - and the LAME version will be "better" because of improvements in psychoacoustics? At least I remember l3enc being MUCH better than anything else at 128 Kbps (Xing lol, cymbal washing anyone?) before LAME came along.