The Forge VTT offers hosting for Foundry VTT, but the two are not inherently linked. We do not sync data between Foundry VTT and The Forge without user intervention. Foundry Virtual Tabletop is an editor without an inherent cloud function- The Forge VTT is the host that brings it to the cloud, and makes it available anytime, anywhere.
What this means is that if you upload a local Foundry world to The Forge and then modify it locally again, you will need to upload this world to The Forge again, to save any changes. Please bear in mind that this will also overwrite any changes made on The Forge VTT.
Needless to say, it’s not a good idea, and we do not recommend using your local Foundry installation to edit your content if you are using The Forge VTT.