Does changing the data on leaderstats using local script actually change it? I write a script on local script and tried to test it and it works however the other system which scan the leaderstats data didn't change so I wonder if only the local player can see that the data have change but in reality it didn't.
No. For a leaderstats to save to a datastore it needs a global script else it wont see that there are any changes. That because local script only access the users machine for changes and a global script access the server.