I hope reverendmother or someone as knowledgeable as she will pipe in , but so as to not let this thread die I'll just tell you what I know. I have been both Presbyterian and Methodist at different times (and am still very fond of both churches).
Presbyterianism is so named for its organizational structure. Members of a congregation elect elders and choose their own minister. The congregations are represented by elected persons at the regional Presbytery, and so on until you get to the national level. There are various kinds of Presbyterian churches (PCUSA, PCA, Reformed Pres., for example), all with varying degrees of theological and social conservatism. It has its roots in Calvinism.
Methodism was so named because the founder, John Wesley, thought there was a proper method for worship and a most successful method of working out one's salvation. The order of worship in a Methodist church is a lot like in the Presbyterian church. Sing a few hymns, greet your neighbors, choir gives special music, pass the plate, recite the Apostle's Creed and the Lord's Prayer, listen to a sermon, sing the Gloria Patri and the Doxology(not in that order). IN the Methodist church, bishops assign ministers to congregations and the ministers stay 5 years.
Whether or not they are liberal is sort of dificult to say. Certainly they did not start out liberal! John Wesley and his brother Charles wrote some of the greatest hymns of the faith that spoke in no uncertain terms of sin, Hell, and redemption. Presbyterians were big into doctrine. Theologically, they both do affirm that Jesus is God's son, fully man and fully God, born of the Virgin Mary, crucified for our sins and rose from the dead. And that the chief end of (wo)man is to glorify God and enjoy Him forever. Their statements of faith are very scripturally solid.
It really wasn't until the turn of the last century that the mainline denominations sort of began to drift away from the historic traditions of Christianity and began compromising with Modernism (with the exception of the Southern Baptists, that is). It was during this period that the evangelicals came out of mainline Protestantism and started their own churches. I guess you could call Pres. and Meth. 's liberal churches even though their statements of faith still look pretty fundamental. And it depends heavily on what part of the country you're in. But in general, there are many women elders and ministers; you never hear about hell or salvation in a typical sermon; youth programs don't tend to be focused on discipling the kids but on providing a wholesome atmosphere. They are starting to be more concerned with being "seeker-friendly" because they are losing membership rapidly. They are eliminating some classic hymns from the hymnbook and re-writing some. Every year a vocal minority in the Pres. church tries to get the nt'l leadership to vote that ministers and church leaders no longer need to be either single and chaste or marrried and monogamous, but this is routinely voted down.
I think these churches tend to be more socially liberal these days because their members tend to be more affluent.