Hatha yoga really just means the physical practice of yoga (asanas as opposed to, say, chanting). Hatha yoga now commonly refers to a class that is not so flowing and bypasses the various traditions of yoga to focus on the asanas that are common to all. It is often a gentle yoga class.
Teachers lead classes that flow from one pose to the next without stopping to talk about the finer points of each pose. That way, students come away with a good workout as well as a yoga experience. If you’re new to yoga, it is a good idea to take a few classes in a slower style of yoga first to get a feel for the poses. Vinyasa flow is really an umbrella term for many other styles. Some studios call it flow yoga, flow-style yoga, dynamic yoga or vinyasa flow. It is influenced by ashtanga yoga.