Should a return button go back or forward?

When implementing a button which takes the user back to the previous page, should I make it go back in the browser history or should it go forward, the same way it does for regular links?

The browser history buttons apply to the browser's history. But I'm quite unsure buttons inside a website should behave the same. For example, if I come from website A to website B, on website B there's a return button and I click it, I don't think it should take me back to website A. It should take me to the homepage of website B, because it's a navigation button specific to website B. However, if I use the browser history button to go back, it should take me back to website A, because it's a navigation button specific to the browser and all the pages it visits.

Is there any consensus on this matter?