There are two paramount differences between art and science. The first is that art is subjective while science is objective. The second is that art expresses knowledge, most often in the form of subjective representation, while science is the system of acquiring knowledge. Art and science are therefore in fundamental character very dissimilar.
Science is concerned with general truths about the operation of general laws pertaining to the physical (and quantum) world and relies on methods of study and data accumulation based on observation and experimentation. The primary method is called the scientific method, which not only allows for methodical knowledge collection but also allows for confirmation of knowledge as other scientists replicate and corroborate observations, experiments, results, and conclusions.
Art, which transcends historical and cultural features and therefore has trans-historical and trans-cultural characteristics, is concerned with aesthetics and is said to have a relatively "stable aesthetic core" united with perceptual properties. This definition roughly covers varying traditionalist, conventionalist, contemporary, and functional definitions of art. Aesthetic is a heightened sensitivity to "beauty" and "good taste."
"Beauty is in the eye of the beholder", art is about individual perceptions. When we look at a painting we all see something different. In this example, images provoke emotions, art elicits more of an emotional response, science does not. Science is more regimented with rules, procedures, and policies to follow. When you look at a cell under the microscope you see what you see and the next person will see the exact same thing, assuming they know what they are looking at.
You could also look at it this way. Major league baseball pitchers use the science of physics when they throw a curve ball, but actually throwing a good curve is an art form.
In many ways they are actually connected and related to each other.
There are also many differences. I would say that the main difference between art and science is that art is more focused on the perception of the world through the eyes of a particular individual. It involves emotions as well. It can be based on personal experience, opinions, etc. Science, on the other hand, is very systematic. When people perform scientific investigations the purpose or goal is to find an answer to something in a very planned out and specific way using the scientific method.
I think the best way to think of the differences between art and science has to involve a discussion of expectations.
In art, the emphasis is on the subject's awareness/past experiences/competence/sensibility.
In science, we expect that the information is discursive/objective.
However, there is a phase during science research when there isn't enough information and the number of possibilities are too great. So, a scientist, who desires discursive/objective knowing, has to use his artistic sensibility to narrow the number of possibilities.
So in fact, depending on the type of science on practices and how you define boundaries, art and science are the same or they are separate.
Goethe sought to nurture and develop that subjective aspect of science, which he considered was constrained by natural laws. So in essence, the subjective is objective to the best trained. It is only the fallibility of the human condition that makes them different.
Art and Science can be viewed as occupying discreet but overlapping sections in Information space. Imagine that the Information space is a sphere and all information can be placed somewhere in the sphere according to cetain characteristics. Each pience of "art" would be clustered towards one part of the sphere and each piece of "science" would be clustered towards another part. But these parts overlap.For example, consider a patent for a scientific process. The document itself is literature and is required to be judged as such on its literary merits alone. If the patent is challenged the literature must be self supporting. On the other hand the patent provides exclusive access to use the scientific process described according to the claims within the patent. So the art supports the science and the science is the reason for the art.
Perhaps medicine is an easier example. Medical practice is both an art and a science. The two can not be separated without destabalising the system.
Science is the universal objective system which is used to build and organise knowledge. Science can be used to explain and predict happenings. Aristotle described science as knowledge that can be logically and rationally explained. Art is the arrangement of items (such as words, colours) in order to affect the senses (often with the hope of an emotional response.)
Art is when you physically do something, say for example, draw a picture (well, it is the art I am thinking of). Science deals with chemical compounds and the earth. It also deals with weather and outer space.