Moral progress ocurrs when what we care about better tracks what actually matters, and when our actions better achieve the outcomes that matter.
According to [[Moral realism]], moral truths are independent of what we care about, and so one can tell a story of progress.
According to [[Subjectivism]], moral truths are grounded in what we care about, so one can only tell a story of progress relative to cares we take as fixed. On this picture, a longtermist might realise that they care about welfare, and then realise that there is much more potential welfare in the future. The correction is self-correction, by one's own lights. The process can involve getting clearer and more informed, or an aesthetic reshaping.