There are so many different styles and kinds of yoga I’m not sure you could even list them all. Even within the same style each teacher teaches differently enough that you could say each teacher really does have a style of their own.
There is a big difference between traditional and modern yoga though. This is my take on it:
Traditional yoga classes are typically 90 minutes. They are held in a studio which generally does an amazing job of creating a restful atmosphere. You need to arrive 10 minutes early at least and I always feel it appropriate to whisper for some reason. Traditional yoga often can include chanting and more advanced breathing practices so be sure to read the class description if you aren’t comfortable with that. You sign up for a period of time or a session of classes. The studio’s are great because they have a large amount of different types of props for customizing poses. The studio’s are also very good at cleaning the mats and other props. Traditional yoga doesn’t always follow current alignment principles – for example many poses bring your knee forward of your ankle. Just be sure to be careful and listen to your body. The costs are higher to attend classes in a studio setting. Look into the teachers teaching credentials as there is no standard as to what level of training private studio’s need. They could be anything from a student teacher to a 500hr Registered Yoga Teacher.
Modern/Fitness yoga classes are typically 60 minutes. They are held in a gym or community center setting. Depending on the teacher they can try to set the mood but very often these facilities do not have dimmers and sometimes it’s not even a fully enclosed room. I have often taught in a studio area baking onto the racquetball court – a test in concentration to say the lease. Very often participants are running in right as class starts. These classes can be drop-in, sessions or part of a gym membership. These facilities very often don’t have props or even an yoga mats so call ahead to find out. I suggest bringing your own to a fitness yoga class. Modern/Fitness yoga is more aware of current fitness principals such as alignment. This type of yoga is a cheaper than traditional but be aware that the instructor may or not have the same credentials as a studio. To teach in a fitness facility you only need to have the BCRPA (British Columbia Recreation and Parks Association) Yoga leader designation or equivalent in your province or state.
The above might on the surface a bit bias toward the studio setting but that is not the case. I suggest trying a variety of facilities, styles and teachers before settling on one you want to invest your time and money into. Even after you find that magic place and teacher be sure to visit other classes.
If you want to try yoga but can’t fit in a 90 minute traditional class please don’t hesitate to try a nearby gym or community center. The benefit are amazing!