What is the difference between Twitter tweet and follow button?
Basically a twitter tweet is a post that you create which could be plain text, text with url, image or even video. Or if they share your blog post on their twitter profile, that's a tweet.
A follow button is simply that, a button people click to follow you on tweeter so that they can see your posts/tweets on their newsfeed to stay updated about you or your business.
Which button I should put on my site for traffic and new visitors?
Use both, below each blog post and on the sidebar as well.
Buttons make it easy for people to share your content, which will result in more traffic for you.