There is no real big difference though I wouldn't use rely on as much with inanimate objects. For example I can depend on my computer but I wouldn't rely on my computer.

There is a different usage for "depend on" so this "depends on" how you have seen it being used. 1. Whether or not your lamp will turn on depends on (is dependent on) whether or not you have plugged it in. 2. The correct answer to a question depends on the meaning/intent/context of the question. In this usage, "Depends on" means that the outcome, or the answer, is dependent on preceding factors or intent. We also say, "It depends..." - meaning that we need more contextual information before we can accurate form a conclusion.

In most context they are the same. The nuance is this, "rely" means that you don't have the ability to do it and need the help of someone else. "depend" is that you are capable of doing it but unable to do so because of some other reason.

both are synonym and mean trust in . for example : my family depends on me .(RELY ON, lean on; count on, bank on, trust (in), have faith in, believe in; pin one's hopes on. )