There are many types of Yoga, but here I will focus on introducing you to seven of these, including Ashtanga, Hatha, Vinyasa, Bikram, Yin, Restorative, & Yoga Nidra.
Ashtanga Yoga, the physical Asana practice, follows a specific series of poses in a specific order. The order never changes, and Ashtanga Yogis always practice while using the Ujjayi breathing technique. Serious Ashtanga studios are very strict. If a Yogi cannot perform a specific Pose, they are to stop their practice and try again next time. Less Strict studios will allow Yogis to continue their practicing using modifications where needed. Ashtanga is the most difficult series of Poses in Yoga.
Hatha Yoga, the physical practice, is defined by slower transitions and holding poses for longer periods of times. Hatha means Sun & Moon in Sanskrit and is supposed to help balance the sun and moon (male and female) parts of ourselves. Hatha Yoga is excellent for beginner Yogis as it allows them time to adjust and create muscle memory for the poses.
Vinyasa Yoga is a swift practice, spending one breath length in each pose. This means in a Sun Salutation; you are only in each Asana for one breath either in or out. Many teachers will prompt their students to take a Vinyasa, which is a smooth transition of the following Asanas together: Chaturanga, Upward Dog, Downward Dog or Plank, Cobra, Downward Dog. Vinyasa Yoga is great for experienced Yogis who know have the muscle memory for correct posture.
Bikram Yoga is a type of Hot Yoga. It is a specific series of Asanas created by Bikram Choudhury performed in a room heated to high temperatures. It is in the Hatha Yoga family. Hot Yoga is amazing to get deeper into postures, however there is massive controversy with this style of Yoga due to Bikram Choudhury himself. Bikram was accused of sexual assault and harassment and even has a Netflix documentary that explains it all.
Yin Yoga is a much slower-paced style of Yoga where the Yogi holds the posture for a minimum of 3 minutes. Props such as bolsters, and blankets are often used in Yin Yoga. Yin Yoga is designed to stretch the fascia, ligaments, and tendons as opposed to muscles. Restorative Yoga is similar to Yin Yoga with one main difference. Yin Yoga stretches fascia and Restorative Yoga is meant to restore the body.
Yoga Nidra is also known as Yogic Sleep, where the Yogi is in the stage of falling asleep but is still awake. They are usually guided there by a teacher, known as a guided meditation. Often the teacher guides the Yogi through each bone and muscle of the body, instructing them to focus on that body part and then allow it to relax and melt into the mat. Yoga Nidra is an excellent way to achieve calm and relaxation.
I hope this explains the difference between the styles of Yoga and helps you decide which style is best for you.