These are the types of recessions according to economists worldwide; i.e. L-shaped, V-shaped and U-shaped ones.
L-shape recession is a recession that goes down and then stays there for a long period of time without a recovery. It could last for 20 years like it happened in Japan. A V-shape recession goes down pretty fast and recovers in very less time. A U-shape recession goes down slowly and then stays there for a few years before recovering slowly. It could last anywhere from 2-10 years, like in the 70s in US where it lasted for 8 years.
Most of the times, it is the economic policy adopted by a government before recession, which determines what type of recession it is; where wrongly calibrated economic policies leading to L-shape recessions, the worst of all.