No, John the Baptist and John the Evangelist are different.
John the Baptist was Jesus’ cousin, and he baptized Christ at the beginning of His (Jesus, that is) ministry on earth. John was later beheaded by Herod at the request of Salome, his stepdaughter. John had been imprisoned for preaching that Herod was wrong to marry his former sister-in-law, which John considered incestuous. John is thought to have been an Essene, a first century religious group roughly equivalent to a monastery. His message was apocalyptic, preaching that “the kingdom of God is at hand (nearby)”. He told his disciples, of which he apparently had a few, that Jesus was the Messiah. The death of John the Baptist was apparently a shock to Jesus, who withdrew to a different part of the country upon hearing about it. It may have been Jesus’ first realization that His mission was to die.
John the Evangelist is traditionally identified with John the apostle. This is “the disciple Jesus loved”, apparently one of His favorites in the inner circle of apostles. His brother was James, and their father was Zebedee. (Jesus referred to them as the Boanerges, a Greek word meaning ‘sons of thunder’, because their father made such noise when they left the fishing business to follow Jesus. )
John the Evangelist is traditionally described as the author of the Gospel of John, the letters of John (I, II, and III John in the New Testament), and the Revelation to John, the last book of the Bible.
Evangelism is not a specific style of preaching. Evangelism means the spreading of the “good news”, that is, attempting to win converts to Christianity. All parts of the Christian church are supposed to do this. My denomination is the Evangelical Lutheran Church in America, which means that we attempt to make converts. Different traditions have different ways of evangelizing, from door to door witnessing (I have done this) to public preaching, to acts of mercy which bear witness to the love of Jesus for all people.
Baptism is the ritual of initiation into the Christian church. It consists of sprinkling water on the head or, in some traditions, completely immersing the baptizee in water, three times “in the name of the Father, and the Son, and the Holy Spirit”. This is a symbolic washing away of sin and drowning of the old, sinful self. Some traditions (like mine) do it to infants. Others, such as many Baptists, do it when the person is old enough to decide for him or herself that they want to be Christian. I lost my taste for discussions on the topic long ago.
Mormons do lots of evangelism. One of the things devout younger Mormons will do is a two year missionary trip around the country. Buy a house and stay there for a while. You are likely to have a couple (they always travel in pairs, wearing white shirts and ties, carrying Bibles and/or the Book of Mormon, another of their Scriptures) stopping by sooner or later.
Don’t rely on any history you get from The Last Temptation of Christ, which is a work of fiction.
Is this the sort of thing you were interested in? Feel free to ask if you want more, or if any of this is not clear.
Yours in Christ,
Shodan