Say I have a 10 of coins that could either be red or blue, and heads or tails. This has 20 bits of information.

My friend is interested in knowing about which of them are heads or tails, but doesn’t care about the color. I then decide to only tell my friend the heads/tails information; so, 10 bits of information.

Another example: With image compression, there's a big difference between "Accurately reconstruct this image, pixel by pixel" vs. "Accurately reconstruct what the viewer would remember, which is basically just 'Lion on grass'".

I’d feel uncomfortable calling this translation “compression”, because there was definitely intentional information loss. Most of the literature on compression is about optimally maintaining information, not on optimally loosing it.

Are there other good terms or literature for this?