Mobile and Tablet responsive in Elementor but not on the actual site?

This happens because of the theme which may have 769px breakpoint while for Elementor it is 768px. You can switch your theme to Hello https://wordpress.org/themes/hello-elementor/ which is official Elementor theme. If this works well then you can change the breakpoint of Elementor to match with your theme. You can give this a try – https://elementorresources.com/tutorials/how-to-change-the-tablet-and-mobile-breakpoints-in-elementor/