Importing old posts to new theme

Was hoping to get some clarification on this topic. What is the easiest way to move old posts to a new theme? I’ve read about wp_posts and the mysql database (or are they the same thing), but I’m a little confused on which one I need to move from the old theme, to the new.

Am I understanding what wp_posts affects: posts and navigation menu? At one point in my experimenting I had seemed to have gotten the posts moved over but my menu wasn’t working (using pixopoint drop down menu).

Thanks in advance!