这里收集了一些老外自己的解释，各位可以读一下，然后自己总结一下：
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.
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.
Their meanings are similar but "count on" and "rely on" are used more on people being dependable... whereas the word depend also has the meaning of "determined by".
Eg. "Can you finish this for me?"
"You can count on me!"
"You can depend on me."
"You can rely on me."
(these all mean you can trust that person to finish it for you)
When using depends as "determined by", you can use it with words like on, what, when, etc.
Eg. "Will you make it to the party tonight?"
"It depends when I finish work."
"It depends on the time."
"It depends what my plans are for tonight."
So whether that person makes it to the party or not depends on (is determined by) their situation.
I hope this isn't confusing for you!!
