Calvinism and Arminianism: What's the Difference?

1. Natural State of humanity

• Both Calvinists and Arminians believe that humans are completely fallen (total depravity) and cannot do any good in their own power.
• There are some pop-Arminians who believe in complete free will (and are thus Pelagian), but this is not the official Arminian position. 

2. Who is chosen?

• Calvinists believe that God determines entirely who will be saved (unconditional election).  It's called "monergism," since God alone does all the work.
• Arminians believe that God empowers us all to be able to sign up for more grace if we will and that God includes us in his kingdom on the basis of our response to his call (conditional election). It's called "synergism" because, by God's grace, our wills work together with his will.  
• Wesleyan-Arminians call the grace that reaches out to us in our powerless state, "prevenient grace."

3. For whom did Christ die?

• In the most stereotypical version of Calvinism, Christ only died for those God has predestined to be saved (limited atonement).  There are "four point Calvinists" who would say Christ died for everyone, although obviously only those whom God has chosen will receive the benefit.
• Arminians believe that Christ died for everyone and that anyone can potentially be saved.

4. Can we reject God's grace?

• Calvinists believe that, if humans could say no to God, it would undermine his sovereignty or authority over the creation.  Therefore, they do not believe a person could reject God's grace (irresistible grace).  And it is only natural that, if God chooses who will be saved, that such people will be saved and make it to the end (perseverance of the saints).
• Baptist Arminians potentially fall into a gray area here.  Once a person is "in" the people of God, they do not believe a person can fail to be saved (eternal security).  Many Baptists would no doubt say that a person who went apostate after conversion was probably never truly saved in the first place (related to perseverance of the saints).  But you do sometimes hear the pop-Baptist position that, even if you tried to reject God's grace after salvation, you could not.
• Wesleyan-Arminians believe that God, in his sovereign will, has made it possible for a person to be "in" and yet later reject God's grace (cf. Heb. 10:26-29) and thus not make it.