note: The so called 'on-line' release obviously requires a web-browser to be run and it is actually a hosted copy of the Web-browser based release. This release can also be downloaded from the Releases section of the project's repository and run locally on your machine, they are the ZIP files without an operation system in the file name.
The Web-browser base release uses your selected web-browser's Local Storage to store all the META data (Passages) of your Story Project, and by default the web-browser's Local Storage area is limited in size to between 5-10MBs (depends on the brand & version) which means you are limited if you want to embed media files within the Passages of your story. The Local Storage are can also be effected by the "Empty Cache" (or similar concepts) feature of the web-browser (depend on brand & settings) so it is recommend to regularly use the Twine 2 Archive option to backup all your projects in one go, or to use the Publish to File option to create locally stored HTML files for each of your projects.
The Install-able release stores each Story Project as a local file in a automatically pre-determined location/folder on your local machine, this location should NOT be used by you as a destination for the Story HTML file you create using the Publish to File option or you could end up overwriting (and losing) your projects. Because this release uses local files for storage then the limits on embedding a media file in a Passage is removed.
Beside Story Project META data storage there isn't any real differences between the two releases.