What is the difference between 参加 and 参与？ I have been using these interchangeably, until today I was corrected, being told that one "参加活动”， not "参与活动“. I then looked up the definition, but it wasn't too helpful. How do I know when to use which?
参与，亦作“参预”或“参豫”。预闻而参议其事；
参与，also as “参预” or “参豫”. Listen something and talk about something.

参加。指的是以第二或第三方的身份加入、融入某件事之中。
参加 means join in something as a part of it.

So, mostly, 参与 has a meaning of organize some people and plan something,
it often has a mean of initiative, such as:
他参与了此次军事行动的谋划工作。(Which means he is one of the commanders.)

As for 参加, which is just join in something as a guest or [third] part people, such as:
他参加了此次军事行动。(Which means he may be just a soldier.)

Besides, we often say : 这个事情我不参与. means do your own business, I don't care about it.