If the theme you are using supports the "editor-style" functionality then you will need to create or edit the existing editor style sheet to give a similar "look" in the visual editor.
Generally speaking, look in the themes functions.php file for the following (default) line(s) of code:
// Add theme support for editor-style
add_editor_style();
IF the above exists, look for the (default) editor stylesheet 'editor-style.css' and make your style edits there.
Of course, if the theme does not natively support the above functionality you can easily add it to the theme or better yet create a child theme and add the functionality that way to insure when the theme is updated your edits are not over-written ... and don't forget to make back-ups first.