The correct usage for buttons and their HTML markup are a hot topic at the moment for accessibility. It has a big impact on how people can interact with your website.
So if you want to ensure you are making the correct choice when using buttons on your website, and know why, then I recommended checking out a couple of resources from the recent @FrontendMasters newsletter which I found useful.
Eric Eggert wrote Buttons vs. Links No, they are not the same. Which explains the differences in approaches and why you should care.
Manuel Matuzović created The Button Cheat Sheet, which gives some really helpful examples of good and bad approaches to button implementation.