Same concept as 720p vs 1080p but not exactly. Audio can be compressed in the same way that video can; certain flavour gets lost for the sake of smaller file size. In video, that means loss of colour spectrum, visuals aren't as sharp and even artifacting when pushed too far. In audio that translates to loss of range so certain instruments can completely disappear from a song, other instruments aren't as crisp and so on. Depending on those $20 headphones, you might be able to make out a difference. The earphones, it's much less likely. There are some $20 earphones such as KBEars which are far better than they have any right to be and make being an audiophile more accessible, if it ever tickles your fancy.

Two simple facts of good audio: 1: Good audio stays good so no need to worry about age so long as equipment hasn't been abused. 2: You can only spend so much before you get diminishing returns.