What is the difference between a minor and diminished chord?

Both minor and diminished chords share a flat third. The difference is the diminished chord also lowers the fifth.

Minor: 1, flat 3, 5
Diminished: 1, flat 3, flat 5

That one change in the fifth makes the sound noticeably more tense. A minor chord feels dark but settled. A diminished chord feels unresolved like it needs to move to the next chord quickly. You'll rarely hear a diminished chord played for long.

On a chord chart, diminished is written with "dim" or with a small degree symbol after the chord name: "Bdim" or "B°". "dim" is the most common label you'll see in worship music, and these chords usually appears briefly as a passing chord before resolving somewhere more stable.