Vinyasa Yoga

Sometimes called "flow" or "vinyasa flow" this type of yoga actually does have a flow to it.  You typically move from one pose to the nex,t coordinating movement and breath.  It can be a great combination of strength, stretch and cardio.  Usually a vinysasa class starts out with a down dog or a spinal warm up then proceeds to several sun salutations.  

After that point your body should be warm, you are probably sweating.  The sweat continues with more standing poses and then you eventually make your way to the ground for some stretches, back bends, twists and general feel good stuff.  Oh don't get me wrong, it's still work, but maybe the sweating has lessened by now.  

If at any time you neeed a rest.  Take a child's pose or a down dog.  You can jump back into what the group is doing when you've had time to catch your breath.
 
Coordinating the breath and the movement is a glorious feeling.  Many yogis get hooked on that.
Vinyasa differs from Hatha in that it flows more, has more sun salutations.  A Hatha class may use all the same poses, but it's just a slower paced.  You may hold the exact same pose for a significantly longer time.  It's still fun and challenging, but different.
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I suggest you give them both a try.  See which one works best for you.