This isn't a question of whether a domain or local account was used, but rather what type of program was installed.
Programs installed on Windows computers are either accessible to all users (per-machine) or only the program's installing user (per-user). A software developer decides which it will be when preparing their application for distribution as evidenced by this FAQ entry for Advanced Installer (a software "packaging" system):
Question: How do I make the package install per-user or per-machine?
Answer: In order to allow the user to choose the installation type at run-time add the InstallType dialog to the project....In Install Parameters Page set the install type to: Per-machine if user is administrator, per-user otherwise.
For example, many computer games can be run by any user that logs on the computer, while Windows 8 Metro Apps are only accessible to the user that was signed-in when the app was installed.
The role domain vs. local accounts play in software installation has to do with permissions to modify the computer's configuration. Domain accounts (including those with Admin rights) can be and often are further restricted from making changes to computers that can affect whether (or how) applications behave when installed. Of course, many programs require Administrative rights to install, but there's no distinction between domain or local administrative rights excepting cases where an administrative user account has had some restrictions imposed on it by the domain.
Bottom line: If you can indeed install the program in question, it's up to the software developer whether just you, or everyone that has access to the computer can run the application.