If the subject is clinical trial, then parallel is the same as superiority design. Where two or more groups are followed in parallel and check which is superior to another!

This study design is mostly used in phase II and III of clinical trials. It is easy, applicable to acute conditions (ie. infection or myocardial infarction), universally accepted and requires simple statistical analysis but it needs a larger sample size comparing to other methods such as cross-over design. You can find more information on this topic from this book:

Design and Analysis of Clinical Trials: Concepts and Methodologies

By Shein-Chung Chow, Jen-Pei Liu