Phenomenology entails getting into the eidos or very essence of a certain phenomenon through one's lived experiences. While the case study is an in-depth investigation of specific issues, individual or group, and even event within a specific environment as well as the related contextual conditions, and the involved processes and interrelations.
Phenomenology is not environment and context based. It focuses on the lived experiences of individuals. The point in phenomenology is the experiences of different individuals on a phenomenon.
Case study is a detailed investigation of the development of a single event, situation, or an individual over a period of time. Data collection methods include observations, interviews, questionnaire etc. Moreover, information obtained from a case study cannot be used to make generalization.
Phenomenology is a study designed to understand the subjective lived experiences and perspectives of participants. Interviews are the main method of data collection.
In phenomenological studies, it involves revealing and examining the individual's views in order to understand the behavior of the individual or the situation in which he is present. However, in case studies, I know that it is an effort to systematically analyze and explain an event, a situation or a person in detail using multiple data sources such as observation and interview. I simulate the case study to a bit crime scene review :)