Do the following two sentences mean the same thing?
部下は課長に残業を頼まれました。
課長は部下に残業を頼ませました。
No, these do not mean the same thing.
部下は課長に残業を頼まれました。
部下 was asked by 課長 to work overtime.課長は部下に残業を頼ませました。
課長 made 部下 ask [a third person] to work overtime.
The latter is a "double-causative" sentence involving three people. The former refers to the same event as the following sentence:
課長は部下に残業を頼みました。
課長 asked 部下 to work overtime.