As pitying people, we may feel very bad for our companion, but we also know – and imply – that we haven’t been there, and realistically never will. Pity is what a medieval monarch would have felt for a gangrenous peasant, or what the most popular and attractive person at school might feel for the acned nerd.
Sympathy, on the other hand, implicates a witness in tune to the suffering of another: their pain has been, currently is or could one day very plausibly be our own. We extend our kindness knowing that we are exposed to comparable misfortunes. We are the superiors of those we pity, but the committed equals of those we sympathise with.