I can attest to both of those.
I have a few small burn scars from when I was 6 or 8, which was 1986-1988, and they have continued to fade. Granted, they were 3rd degree burns, so they're still pretty clear, but they are softer and less obvious every year.
And the one scar I have from shaving is a 3/4" long line on the ridge of my right cheekbone. Looks badass.