A static website is where a web developer builds a site from scratch "code wise" and is not changeable without a developers assistance.

Dynamic websites are where you as the business owner, can change your site.

Which does Google prefer?

Google very much prefers the dynamic website, as long as the menu structure at least remains or grows, that is menus are not removed.  Assuming this, Google loves new content, in particular when it is very relevant to how you are displaying your site technically to Google.

So if you have an existing "static" website, now is a good time to consider changing!