Wordpress Visual Editor: How to make it functional with custom themes

We had our company website redesigned several months ago, and it is currently on the wordpress.org platform. It was ‘delivered’ with a custom theme modified from the 2010 pre-existing theme. My question is regarding the web-based visual editor and the corresponding stylesheet (as far as I understand, this is what dictates how the visual editor in the WP interface displays content as it is created). Currently, our visual editor looks *nothing* like what actually appears on the site; fonts, images, sizing, etc., so much so that it is actually easier to work in the html view.  I am guessing that the discrepancy is due to the ‘visual editor stylesheet’ not being updated from the 2010 template theme to reflect the custom theme that was designed for us.  If that is the case, is there a way to easily update visual editor stylesheet so it matches the actual site’s stylesheet?  If my logic thus far has been correct, does this also mean that all changes to the main stylesheet must be duplicated in the visual editor one? That doesn’t sound feasible, so I am obviously missing something!  Any advice would be greatly appreciated.  My apologies if the question is confusing; I am happy to clarify/provide any additional details needed. Thank you in advance!