Is there a difference between "Father" and "Reverend"?

We have two priests in our parish; one goes by Father, the other by Reverend. Is there a difference in these two titles?

Yes. One apparently is being used incorrectly because it should never be used in ordinary conversation. “Reverend” is an adjective that is used when writing out a clergyman’s name (e.g., “The Reverend John Peterson”). It is analogous to using the title “Honorable” for certain dignitaries (e.g., “The Honorable John Peterson”): Just as someone entitled by courtesy to the title “The Honorable” on his envelopes is called (for example) “Senator John Peterson” when speaking face to face, so a priest might be addressed “The Reverend John Peterson” on his envelopes but called “Father Peterson” face to face. And, just as the word “Honorable” must have the word the preceding it, so must the word “Reverend.” Calling anyone or addressing envelopes to anyone as “Reverend John Peterson” is incorrect.