Live examples are those that run inside the app. Some of these examples showcase the latest SwiftUI features, therefore, they may require the latest macOS version.
For examples that use SwiftUI features that are still in beta, the live execution of the example may not be available. That will depend whether you are using a stable version of the Companion for SwiftUI app, or a beta version. The difference is one is built with the latest stable Xcode/SDK version, and the other with the latest Xcode/SDK beta.
Because Apple’s App Store does not allow for apps built with a beta versions of the Xcode/SDK, if you are using an app downloaded from the App Store it is a stable version (live examples execution of beta features will not be embedded).
For more information, check the release notes.