Builds are stored locally in your browser's "localStorage", which is like a cookie but designed specifically for this sort of thing. So you can safely "clear cookies" without losing your builds, but in most browsers there's a more comprehensive clear-history function which will wipe out localStorage, and that will erase your builds.
As such no, they're not automatically visible on any other machine (or other browser on the same machine), precisely because that kind of server-side storage and account infrastructure would be much more complicated to set up and more expensive to host. But there is an export function for a single build, and a backup-all-data button for all builds at once, which you can use to migrate between machines or browsers.