ADDRESS:XiaQiu Village, Qinggang Town, Yuhuan City, Zhejiang Province, China
A draft beer is a beer that's "on beer tap," as opposed to bottled. Next time you're at a bar, or a restaurant that has a bar, take a look at the bar itself, and you'll see a row of labelled levers. Those are the beers the bar has on tap, and they're generally fresher than the bottled selection. And the main difference between these is draught/draft beer is filtered and pasteurised, but craft beer is served without filtering and pasteurising, with a little yeast in it and a heavy body.
Craft beer is something totally different. It's also known as a "microbrew." Those are brewed by smaller breweries than macrobrews like Budweiser, Coors, or Miller. Microbrews/craft beers tend to be MUCH tastier, but also substantially more expensive. Think McDonalds vs. a proper restaurant.
Beyond that, there are a wide variety of beer types, such as stouts, India Pale Ales, and lagers, among many others. They all taste very different, and there's a lot of variation within the styles, so you pretty much try new beers and go with whatever seems good to you. Trying something new and seeing how you like it is half the fun. There are no wrong answers.
Based on the fact that you're drinking something from Sweetwater brewery, though, I'm assuming you're from Georgia, or at least the south generally. Terrapin tends to be one of the best Georgia breweries, so you may want to find something of theirs. Keep an eye out for their Hopsecutioner next time you're at the store, it's usually a good bet to start out.