What is the difference between Presbyterianism and Evangelicalism?

Nathaniel's answer above is the correct one, but I would like to give another perspective. I think it is worthwhile to contrast writings of Presbyterianism's biggest hero (John Calvin) with modern teachings from Evangelicalsism's biggest hero (Billy Graham, or at least his website) to draw some distinctions.

To get a good summary of the soteriology of the great Billy Graham I visited this page of his website: http://billygraham.org/story/have-you-heard-the-good-news-of-salvation/. I then clicked the link at the bottom that read "Follow the Steps to Peace now" and was redirected here http://peacewithgod.net/. At this site I was told how to obtain salvation:

We can’t earn salvation; we are saved by God’s grace when we have faith in His Son, Jesus Christ. All you have to do is believe you are a sinner, that Christ died for your sins, and ask His forgiveness. Then turn from your sins—that’s called repentance. Jesus Christ knows you and loves you. What matters to Him is the attitude of your heart, your honesty. We suggest praying the following prayer to accept Christ as your Savior: PRAY NOW

"Dear Lord Jesus, I know I am a sinner, and I ask for your forgiveness. I believe you died for my sins and rose from the dead. I trust and follow you as my Lord and Savior. Guide my life and help me to do your will. In your name, amen."

This is step 4 of a 4 step process; after praying the prayer you are saved, born again. To me this prayer is the contemporary definition and litmus test of Evangelicalism. I think it unites Evangelical denominations like the Book of Common Prayer does Anglicans. By sincerely praying this prayer from your heart it is said that you receive the sacrifice of Christ and are saved. Although I will admit there is probably some variations on this in different denominations; it is the best way I can think of to define what the Evangelical movement is (although perhaps not what it always was).

I think it is easy to point out how this teaching omits certain things in the plan of salvation according to John Calvin.

First lets hear some words on sacraments from Institutes of the Christian Religion Book 4 Chapter 14 Part 7.

the Lord offers us his mercy, and a pledge of his grace, both in his sacred word and in the sacraments, but it is not apprehended save by those who receive the word and sacraments with firm faith

So one should not only receive and respond to the word, but also the sacraments. We also hear him talking about the church in Book 4 Chapter 1 Part 1

What God has thus joined, let not man put asunder (Mark 10:9): to those to whom he is a Father, the church must also be a mother.

We can also listen to his teachings on faith and works; in Book 3 Chapter 18 Part 5 Calvin states that

[faith] saves no man without works

So I think it is fair to say that Presbyterians who adhere to Calvin's teachings will have a broader view of the plan of salvation than many Evangelical Christians do. I would suggest that John Calvin views salvation more as a process, involving the sacraments and good works, whereas Evangelicals tend to emphasize the moment of conversion as the end-all-be-all of salvation. Billy Graham exhorted sinners to receive just the word, John Calvin would exhort them to receive the word and the sacraments. Calvin does strongly emphasize salvation by faith alone, but he doesn't confine the generation and perfecting of saving faith to a single moment or action. Although I will admit that I only really skim the Institutes in order to grab sections that are on topic, I am not a scholar.

As you mention, evangelicalism refers to a movement that typically emphasizes salvation through faith in Christ, the authority of the Bible, evangelism, and a conversion experience.

On the other hand, presbyterianism refers primarily to a form of church government. In this system, elders rule the church – a session of elders is responsible for leading individual congregations, and send elders to regional presbyteries that oversee the churches in their respective areas. Presbyteries send representatives to the general assembly, which oversees and serves as the highest court of the denomination.

It should be clear, then, that evangelicalism and presbyterianism are, at root, independent of each other. That is, only some evangelicals are presbyterians, and only some presbyterians are evangelicals.

Historically, presbyterianism is closely associated with Reformed theology, but this link is not absolute. The Puritans, for example, preferred congregational church governance, though they shared beliefs in Reformed theology with their presbyterian friends. The same is true of many evangelical "Reformed Baptists" today.

Within Presbyterianism, not all would be considered evangelical. Though the borders of evangelicalism can be blurry, the more liberal members of the PCUSA, the mainline presbyterian denomination in the US, would usually be excluded from it due to their views on salvation and the Word of God. US denominations like the PCA, EPC, OPC, and RPCNA, being more conservative, would often be considered evangelical. Outside the US, many countries have "Evangelical Presbyterian" churches, such as Chile, Ghana, and the UK.