That may be the classic definition, but liberalism has changed drastically in the past decade or two. I did not quit on the democratic party, the democratic party quit on me.
And equal opportunity does not automatically mean equal means.
And this is one of the things that I very much disagree with liberals. The government is only and should only be responsible for the bare minimum. Defense, interstates, and a few other things that we probably do not need to get into. Welfare is a responsibility of the community, because the government can not even manage a whorehouse, let alone the other programs that many think they should be involved in.
Today, liberal (as defined by the liberals that the liberals have put in charge) more governmental control, lower state rights, fewer individual rights, etc al.