Bad assumption, it does not. The Froala editor and CSS associated with that editor are NOT loaded on the live site. You need to do one of two things:
- Modify the editor to insert a CSS class you already have defined in your live site stylesheet.
- Add CSS to your live site stylesheet to replicate what the Froala editor has.
You can 100% verify this by navigating to the page in the content tree, then edit it, right click on the table, then inspect. You'll most likely see some stylesheet from the CMS or Froala that is applying styles to that table. Then go and do the same thing on the live site, most likely no styles applied to that element/css class.