Damien's answer may be right but it is not the way I would have interpretted the two phrases. Law(s) of Nature = scientific discoveries/knowledge/rules that tell us how things in nature work, e.g. The laws of nature tell us that all living things need water to sustain life. e.g. The laws of nature require all living things to die one day. Will of Nature ("will" means what nature wants to do / nature's desire) = the predictable or unpredictable events that cause all natural things to grow, remain the same or change in a positive or negative (adverse) way, e.g. The typhoon destroyed our village - it must be the will of nature. e.g. All living things evolve over time. Evolution could be called the will of nature.

The Law of nature is a rule that establishes reasons for human behavior and moral actions. Also, it is based in the content of nature, which seemingly gives it validity everywhere. The Will of nature is an idea that establishes the idea "free will" - the ability to do as one pleases - for any thinking, living thing. These two ideas represent the controversy caused by living, breathing, thinking things. Are their actions and the actions of people dictated solely by nature, or is there some element of "freewill" that arises out of the abyss of natural development.

Damien and Silahtar are both correct when they say that 'nature' is not a living, thinking thing. If nature cannot think then how can it have a 'will' (a desire or wish to do something). The answer is "It cannot." But, in all languages and cultures we assign human charcteristics to inanimate objects (non-living things). e.g. we use the word 'she' when we talk about boats, typhoons, the oceans, even a new car. For example, "Oh, she's beautiful. Oh, she's a big storm. Oh, she's (the ocean) angry. She's (the car) expensive. So maybe it's possible to refer to nature in a non-real way, as if it is a living thing, hence the expression "Mother Nature".

I partly agree Richard. law of nature is its rules which explain how it is going on. but since the nature is not a living and thinking thing it has no will. everything in the nature can be explained by laws so there is no need to its will.

There is no difference whatsoever! They are the same.