They look similar — a surface covered in images — but they answer different questions. One is a design tool. The other is a motivation tool.
A mood board defines how a project should look and feel: the palette, typography, imagery, and tone of a brand, a collection, a room, or a film. It is made to be shared, argued with, and approved.
A vision board maps what a person wants: goals, places, milestones, the life you are aiming at. It is made to be looked at — usually by you, usually on a wall.
If you are building something other people will see — a brand, a product, a wedding, a channel — you need a mood board. If you are organizing what you want from the next year of your life, you need a vision board, and any cork board or notes app will serve.
Traditionally a mood board means hours of collecting and arranging. MoodyBoards collapses that: describe the project in a sentence or two and it generates the board — colors, typography, and original images that agree with each other. Your first board is free, so the fastest way to understand the difference is to make one.