Many tablets are wifi only, but you can get most models with 3g/4g connectivity. You have to pay to have them added to your wireless plan, though. If you're interested in using your phone carrier's network, you may wish to explore their offerings to be sure there will be no compatibility issues.
As far as usability is concerned, yes, an Android tablet works just like a phone. You just wouldn't make a phone call with it. There are lots of Android tablet options. A number of manufacturers add their own customizations to Android (Samsung is one of them) so if you're comfortable with your Galaxy phone, you may want to consider a Samsung tablet. If you're looking for something different, visit a store and get your hands on a bunch of models to see what you like best.