When a project, client, invoice, etc. are active, they are fully functional and usable. They appear in all drop-drown menus and reports.
When they are set to archived, a project, client, invoice, etc. are still active, but they do not show up in the drop-down menus when you create a new project, client, invoice, etc. However, archived items still show up in reports.
When a project, client, invoice, etc. are deleted, they do not show up in drop-down menus, or reports. They can be later activated for use, if needed.
Note: Both active and archived clients count toward your client limit; deleted clients do not.