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These two terms, “evangelical” and “charismatic” may not always be used with precise meanings. The term “charismatic” is usually used to refer to someone who believes in and practices what would be called the “charismatic” gifts. Usually this would mean speaking in tongues, along with prophecy, the interpretation of tongues, and sometimes other gifts such as a “word of knowledge,” etc. Non-charismatics believe that these particular spiritual gifts existed in New Testament times as sign gifts, but that they have now become extinct. Charismatics and non-charismatics would usually agree that other spiritual gifts such as teaching, giving, administration, helps, etc. are gifts that still exist in the church today.
There is usually a certain style of worship among charismatics, which is more energized and which expresses more emotion. It seems to me that over the past 30-40 years some practices and styles of worship that used to be practiced only be charismatics (such as the raising of hands in worship) have now been embraced by a larger group of Christians, including non-charismatics.
The term “evangelical” may refer to a charismatic Christian or a non-charismatic Christian. Essentially an “evangelical” is understood (by Christians at least) as a person who holds to those doctrines that separate Christianity from mere religion – doctrines such as the virgin birth, the full deity and humanity of Jesus Christ, His death on the cross for sinners, and His resurrection. In essence, Evangelicals believe the Bible. Evangelicals believe that all men are sinners, deserving of God’s eternal wrath, and that the only means of salvation is the death of Jesus Christ in their place. They trust in Him as the One who paid the penalty for their sins, and then rose from the dead and ascended into heaven, where He is now with the Father, interceding for the saints.