Nature is observable and everywhere. All life, all elements of the environment, the atmosphere and all planetary phenomena, the entire universe as we know it. This all exists and can be observed.
Natural laws are simply a set of observations that human beings have made about nature. They are, for lack of a better metaphor, the colour of nature. We know that nature works in certain ways and we have chosen to call these ways the “laws” of nature. Come to think of it, it is a rather anthropocentric way of defining the world. Laws are a peculiarly human thing and exist only within human societies. Small wonder then, that we see a reflection of ourselves in nature.
This seems redundant because when we see ourselves reflected in nature, we kind of emphasise the notion of our otherness from nature. In reality, there is no otherness. We are as much a part of nature as grass is, or a rhinoceros is. Human beings are fully included in nature. There is no aspect of the human condition that has ever been observed by science to be beyond nature.
So to answer the question — nature exists. And we exist as parts of nature. The laws of nature are our way of defining nature. In fact, it might be fair to say that the laws of nature are nature.