Dialogue abruptly cut off by new speaker and then resumed.
When a new speaker interrupts the first, use the em dash where the first speaker’s words are interrupted and again where they resume.

“He is leaving—”
“But I’m not ready to go yet.”
“—to get Ann’s gift.”

Dialogue that trails off.
When dialogue trails off, usually when the character has lost his train of thought or doesn’t know what to say, use the ellipsis.

“He is leaving …” OR “He is leaving …” she said.

If you want to read more dialogue tips, check out our blog article Five Common Dialogue Mistakes Writers Make.