Twine 2 can be accessed online.
Twine 2 can also be downloaded and run on Windows, MacOS X, and Linux systems. The latest releases on GitHub has a listing of the current versions per operating system.
Twine 1 is only a desktop application. While it can still be used, it is not currently maintained or under active development. The current version is 1.4.2. The IF Archive retains builds for Windows and macOS.