Let's compare it with data from the same period.
This product was released around the same time as a competitor's new product.
Similar incidents occurred in various places during the same period.
Compared with works from the same period, his painting style has changed dramatically.
同時代 emphasizes belonging to the same historical era or generation, while 同時期 is more neutral and can refer to any short or long shared period.
同時期 broadly means 'around the same time' in everyday contexts, while 同期 is the fixed term used in set comparisons like 前年同期.
同期 usually means people who joined or graduated in the same year (or technical 'synchronization'), whereas 同時期 simply means 'the same period of time' in a general sense.
Compound of 同 (どう, 'same') + 時期 (じき, 'time, period').