A Trailhead Playground is a free, online learning environment that allows you to try out Salesforce features and apps. You can use a Trailhead Playground to test out an app from the AppExchange before you install it in your production org.
A sandbox is a copy of your production org that you can use to test changes and new features. You can install an app from the AppExchange in a sandbox to see how it works in your environment.
Testing an app in a production org is not recommended, as it could affect your live data. Checking edition compatibility is important, but it is not a way to try out an app.