Below are the most common types of yoga explained as simply as possible.
Hatha Yoga will be any form of asanas (or poses). Hatha classes now are usually gentle and performed at a slower pace. All the following styles are, therefore, in a way rooted in Hatha.
Vinyasa (also called Vinyasa flow) is a sequence of asanas distinguished by fluidity through the transitions. Asanas will be linked by interconnected poses that will be performed multiple times during the sequence, increasing heat in the body. The choice of the asanas will vary from teacher to teacher.
Ashtanga vinyasa - often just ‘Ashtanga’ is a structured sequence of asanas, primarily focusing on breath and strength. This practice would therefore be described as repetitive (because you follow the same sequence) and rigorous.Traditionally one can only practice the second series of poses only if the first one is mastered.
Restorative (also called Yin) is a slow but deeper approach to asanas. In restorative, practitioner will use props such as blankets, blocs and straps. There will be a little set up for each pose in order to be comfortable holding it for a longer period of time (3-4 minutes or more). The practitioner will therefore have more time to release tension and still the mind.
There are more types of yoga practices but the above ones are the most common ones you will find in studios and gyms.
They all have the main benefits in common, increase of flexibility and strength, bring calmness, so whichever appeals to you, just give it a go!