I think for the most part they are pretty similar, but "by the time" usually seems that an action has taken or will take a certain amount of time to be completed. And simultaneously another action will also have been completed or is beginning. Example By the time you finish your dinner dessert will be ready. By the time I arrived at the house, he had already left. When seems to be more conditional. When is usually followed by a request or some kind of information. Example When you finish your dinner, you may have dessert When I arrived at the house, they greeted me. But sometimes they are both interchangeable.

BY THE TIME There was hardly any guests left by the time we got there. 我们到那儿时客人差不多都走了。 It was closed by the time we arrived at market. 等我们到时市场已经关门了。 By the time I got home, she was gone. 我回到家时，她已经走了。 I hope it helps you!