What is the difference between Presbyterianism and Evangelicalism? I understand the main differences with Evangelicals vs. protestants are the strong beliefs in being "born again" and Biblical fundamentalism.

However, what are some of the main differences in theology, personal belief, politics, structure of leadership and interpretation - specifically speaking between Evangelicals and Presbyterians?
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.