Well, David B., to put it simply, Lutherans and Presbyterians are considered Christians.
Christianity is a faith based on the teachings of Jesus Christ, and the most orthodox/conservative (I'm not talking about Orthodox Churches) believe the following:
1) Jesus Christ was God and man simultaneously.
2) You must believe in Jesus Christ as your Lord and Savior to go to heaven.
3) The Bible is the infallable word of God.
Everything else aside from those three things is up for debate (and the most liberal of Protestant denominations would even argue about the validity of those three.) I'll give you a short history of how things came about:
The original Christian church became what we know as the Roman Catholic Church. Early on in Christian history, when Christianity became the state religion of the Roman Empire under Constantine, (I'm not sure at what time) there was the first Great Schism in the church which created the (mostly geographical) separation between the Roman Catholic and the eastern Orthodox churches. While Roman Catholicism dominated western Europe, Orthodoxy dominated far-eastern Europe and Asia Minor.
Later on, at about the same time as the Renaissance in arts, the Reformation began. Reformers were called "Protestants" because they were protesting against excesses in the Roman Catholic Church such as the sale of indulgences. Martin Luther was perhaps the most vociferous of the Protestants, and those who followed him out of the Roman Catholic Church were called "Lutherans." Even today in Germany you will still find that northern Germany is heavily Lutheran while southern Germany is generally Roman Catholic.
Another Protestant was John Calvin, and those who followed him were "Calvinists." The Calvinists in Scotland called their church the "Presbyterian" and adopted a statement of beliefs called the "Westminster Confession."
Other Protestant groups include the Dutch Reformed Church (Calvinist), the Methodists (lead from the Anglican Church by John Wesley), the Baptists and pentacostal churches.
In the U.S., the Anglican Church is called "Episcopal." Anglicans are also known as The Church of England -- which was formed when King Henry VIII decided he wanted another divorce and the Archbishop of Canterbury wouldn't grant it. King Henry VIII declared that England would no longer be Roman Catholic and installed his own Archbishop of Canterbury, which is why that is still today the highest leader of The Church of England. Some Protestants do not consider Anglicans/Episcopalians to be true Protestants due to the lack of Reform theology incorporated into Anglican traditions.
So, in short, your Lutherans follow the teachings of Martin Luther and your Presbyterians follow the Westminster Confession. Protestants and Roman Catholics differ in theology based on the teachings of the Reformation, and the Orthodox Churches are very similar to the Roman Catholic Church except that they don't follow the Pope in Rome.
Part of the reason I know a lot about this is because I've been a member of several different churches! I was baptized as a Lutheran, was raised in a United Methodist church, and as a teenager my family then joined a Presbyterian church. Now I attend a pentacostal church affiliated with the Assemblies of God (when I can drag myself out of bed on Sunday morning!) I am a Christian and I believe the three points I laid out above. For me, personally, it isn't important what's on the door -- it's important that the people believe those three things, and that they love God enough that it shows in their every action.
If you want to e-mail me, my e-mail address is in my profile. Rather than that, go to your local library and look some of this stuff up, usng the terms in the descriptions above. Or I can also suggest a Protestant website that might be helpful (aside from its relatively conservative bias) -- http://www.gospelcom.net
which is one of my favorite reference sites.