Local storage question

I created an index page in HTML. Using JS, I save data to local storage. The code works and each time I change a field and press the button it updates local storage.

However, if I open up the same index page in Fire-fox and in Google Chrome, changes made within each browser seems to update different stored data. It appears that each browser has its own memory location even though I use the same computer.

Is this the case? Is it possible to have two different browser instances of the same page access and update the same local storage?

no, local storage is just for the single browser, and until local storage is cleaned

if you want data to stay between different clients you need to implement a back-end

Thank you for your response.