“在过程中”表示：从一个事情发展到另一个事情所经过的程序，表示一个阶段； “在期间”表示：在某一完整时间段内所发生的事情。

as every time with Chinese -- depends on the context here we say it and there we don't no "rules" with vocabulary

在A的过程中 vs. 在B期间 A强调动作，B强调时间

在 过程中 equals in the process of /in the procedure of, 在 期间 equals during the period of. The former means there are must successive actions or operations，and usually it must be human to do these actions, while the latter only describe simple time duration, no matter whether there are things happened in this period. I will give you some example, you could notice the slight difference between them. firstly:在这道菜的制作过程中，厨师长一直在关注着每一个细节；在陶器的烧制过程中，温度是至关重要的；在开车的过程中，司机不能打电话，否则会危害公共安全。secondly:这个罪犯在服刑期间，表现良好，警察局决定缩短他的服刑期；长假期间，我一直呆在家里，什么事都没干；根据天气预报，明天1点到5点期间，会有大暴雨。