The participatory spaces house your participatory processes. Each participatory space has a presentation page, arranged differently according to the type of space. There are 4 types in Decidim.
Processes are adapted for the implementation of a time-bound participatory mechanism, with stages (participatory budget, classic consultation with proposal collection/voting for example, etc.). To find out more about Processes, click on this link.

Examples
The Citizens' Convention on Climate has used Processes as a thematic space for contributions.
The Swiss city of Lausanne uses Processes to involve citizens in the development of their urban activities.
Assemblies are better suited to participatory governance over a long period of time. It is also possible to create sub-assemblies and/or link a assembly with a process.
Assemblies can be useful, for example, for setting up a participatory mechanism within an organisation, allowing for the creation of working groups/sub-groups via sub-assemblies. For more information on assemblies, click on this link.