So, "It's clear to me" means "I have understood what it means" while "I'm clear on that" means "I have made my points clear (so you should have understood)".

What tsuwm said is good advice. But to expand a little, normally one wouldn't claim to be clear in the "you should have understood" sense. You might ask someone if you are clear in this sense but it is a little presumptuous to claim to have been clear implying that the listener is some sort of idiot for not understanding. One might also say something like "I hope I'm clear on this." It's not so presumptive and it gets the point across.