The fundamental difference between art and beauty is that art is about who has produced it, whereas beauty depends on who’s looking.
Of course there are standards of beauty – that which is seen as ‘traditionally’ beautiful. The game changers – the square pegs, so to speak – are those who saw traditional standards of beauty and decided specifically to go against them, perhaps just to prove a point. Take Picasso, Munch, Schoenberg, to name just three. They have made a stand against these norms in their art. Otherwise their art is like all other art: its only function is to be experienced, appraised, and understood (or not).
Art is a means to state an opinion or a feeling, or else to create a different view of the world, whether it be inspired by the work of other people or something invented that’s entirely new. Beauty is whatever aspect of that or anything else that makes an individual feel positive or grateful. Beauty alone is not art, but art can be made of, about or for beautiful things. Beauty can be found in a snowy mountain scene: art is the photograph of it shown to family, the oil interpretation of it hung in a gallery, or the music score recreating the scene in crotchets and quavers.
However, art is not necessarily positive: it can be deliberately hurtful or displeasing: it can make you think about or consider things that you would rather not. But if it evokes an emotion in you, then it is art.