Elementor is a website builder for WordPress. The free plugin lays out pages by dragging sections and widgets, inside a WordPress site the person already hosts. Elementor Pro adds theme building, a form widget, a popup builder, and other tools the free plugin does not include. Elementor also sells hosting as a separate plan.
The plugin does not replace WordPress. A site still needs a domain, hosting, and a WordPress install, unless the plan is Elementor’s own hosting. Themes, popups, and the form widget that stores submissions are Pro features, so a page built with those does not move to a site that only has the free plugin.
The editor runs in the browser against that WordPress site. Choosing Pro is about the widgets and the theme builder, not about a second copy of the pages.