A prophet was a man and a prophetess was a woman. Other than that, their specific calling was the same; that is, to receive direct revelation from God (usually about future events) and to pass that along to others. I know of no scripture that makes a major distinction (other than gender) between a prophet and a prophetess. They both received messages from God and reported them to others. However, we can see a difference in practice. The men were more outward. They often had a special position in the court (as Isaiah). They sometimes would speak to a large congregation (as Elijah on Mt. Carmel).
The prophetess obviously took a less visible role. Josiah sent to Huldah the prophetess and she gave him the word of the Lord (2Kings 22:12-15) Philip had four daughters which did prophesy (Acts 21:8-9), but there is no indication that they went out and preached in any public way. I think the problem comes in the common teaching that a prophet is a preacher of earlier times. True, the prophets did sometimes preach (as we understand preaching). But that was not what made them a prophet. They were a prophet because they received prophesies from God. This gift was given both to men and to women.
To evangelize is to reach out to the lost and strive to win them to the Lord. Every Christian is called to evangelize the lost. An evangelist is someone who has a special calling from God to go to unreached areas, preach the gospel publicly and privately, win souls to Christ, and lay the foundation for new churches to be planted. I say this from a study I did of the ministry of Philip, the only named man in the Bible specifically called an evangelist. Many of the preachers who go to various churches and preach a meeting are not true evangelists because they are not especially going to the unreached lost. I am not accusing them of being wrong. They are often a great blessing to the churches where they go. They just are not specifically doing the work of an evangelist. Perhaps we should find a better name for them. Most likely, we will just keep calling them evangelists.