方法 - method of doing something. Low emphasis on solving a problem. More of a positive / neutral focus i.e. a way to achieve some goal. Implies choice and freedom to act. 办法 - method of dealing with or solving a problem. More negative focus. i.e. a way of dealing with a unavoidable events. Implies less choice in the matter.

也差不多只是听起来会很怪。非要分的话办法可以是对的也可以是不对的，但方法经常是对的。

方法 means a general solution, can be deal with one kind of things, 办法 is just according to one specfic thing

-"I got a problem here, do u have any 办法?" -"no, it is too hard, i have no 办法" ================= -"the 方法 that do this thing is......" ======================== 办法 means something to solve some problem. 方法 means something that u can follow to achieve something. sometimes, they can replace each other.

Although you're afraid you could not understand the answers in Chinese, the Chinese you used in your question is really perfect! Just go, go, go!