Should a sales manager train his team on how to sell rather than how to share the benefits and advantages of his product with the right customer?Why?

It should be the same! depends on how you define selling, Selling process starts with segmentation, target the right segment, then communicate the right message. I think the sales will definitely follow as a result of the good implementation of selling process.   

I believe every leader should train a team in such a way that the team not only knows the benefits of the product/service but also believes in it. The more you believe in something the better and faster you can sell it.