preacher
A person who delivers sermons, typically in a religious context. Can also be used figuratively for someone who lectures others in a moralizing way.
He is famous as a preacher at the church.
The preacher's sermons are always long and boring.
伝道師 is an evangelist or missionary who spreads religious teachings, whereas 説教者 is specifically one who delivers sermons.
Compound of 説教 (sermon, preaching) and 者 (person). The exact historical derivation is straightforward; the word follows a common pattern for agent nouns.