Ah, you should have better posted this as a question, but I can give you my view. Both mean about the same but there is a slight nuance.  Rely on is more ongoing. For a longer period. And less one thing. Example:

1. I can rely on my intelligence to solve a problem when I encounter trouble.

2. Are you coming to the party on Friday? Yes, you can count on me.

In sentence 1, you could also have used 'count on'. In sentence 2, 'to rely on', can be used, but it's a little strange. Like the party is really an important thing, and you can rely on me to help you make a good impression on your boss who is coming too or something. It's a bit overkill.

Thank you for your specific and definite answer.One more question,what is the meaning of "post" in the sentence"you should have better posted this as a question"?