One identical archive serves both Linux and Mac without an associated Java runtime. Extract it and use the included aladin shell launcher. On Mac, the official instructions open the shell launcher with Terminal.
Complete OS-independent Java application. Use an installed suitable Java runtime and launch java -jar Aladin.jar. The WebStart descriptor launches the same Java application and is an alternative launcher, not a separate full program.
Complete Java beta application. Launch java -jar AladinBeta.jar with a suitable Java environment. The beta tests forthcoming features and carries a proprietary all-rights-reserved license, unlike the official GPL release.
