There used to be big issues with something the browser manufacturers called “quirks” mode. Basically, they would try to recognize pages built for older browsers that rendered some things in non-standardized ways, and then emulate these quirks and outright bugs. Modern browsers, like Chrome, don’t try to do this, so old pages might look different than they used to.
Nowadays, as long as you put the HTML doctype at the top of your page (that’s the line <!DOCTYPE html>
at the beginning) every browser should treat your formatting exactly the same, for all time. But I guess we’ll see!