These terms are often used interchangeably but they are actually two different processes.
Co-design, design with users, not for them.
Participatory design you design for users and then get their input.
- Co-design: you ask users to create the questions which are used to ask their own user group for product feedback
- Participatory design: you come up with the questions to ask users for product feedback
Co-design is about building a bridge between yourself who has the expertise in tech and design and the users who have the first-hand understanding of their own needs.
Co-design can involve coaching (I.e what technology and designs are possible within a budget) and involving them at the start of the design process so they can generate ideas to solve their own problems.
As much as possible you want to put users in the driving seat but without there being a need to teach them sketch, photoshop or programming.
In Participatory design, you create the product. This means doing much of the background research, interviews and data collection.
You can then get feedback and input from users as early as possible through focus groups, workshops or user-testing.