Demo is a sandbox environment used for testing. A User can build, create, change, modify and alter any kind of workflow in Demo, and can't "break" anything. Like Production, in Demo, when Users test sending an envelope it does send an email to the person specified though, so in that sense it's real and live. Demo also has some features Production does not because DocuSign wants Users to see and experience more functionality to see if it's something they want to purchase.
Production is the live environment that is also the system of record. Accounts are configured at the Organizational level (from our team) and managed at the Departmental level. Some settings are unique to Departmental Production accounts, like Branding.
Testing a new workflow or building and testing should happen in Demo, especially when a User is working with a new feature, like, say, WebForms. Once it's complete, the User can download the configuration then upload it to Production to use.
Equivalents are things like test kitchens, Demo is like a test kitchen, it's not a live restaurant kitchen.
Demo is also a staging environment, think of it as a rehearsal space before a live performance.
Most if not all software products have a Demo, Sandbox, QA or Testing environment versus a Live Production environment. When it comes to software like UCPath (PeopleSoft), their QA environment is where they test a payroll run, but no one gets paid. UCPath Production is where payroll is run, and emplioyees are paid.