What's the difference between believe and trust？

[Okay, maybe Mike Johnson is a competent parliamentarian.]

To believe something is to take it for fact; to trust something (or someone) is to believe it in a situation in which others might find it dubious or disputable. One also often trusts people to do something--"I trust my spouse to be faithful to me", or "I trust Pelosi to get the American Families Plan through the House".