Speaking in very broad brushstrokes (where would the fun be otherwise?), there have been two different ways to approach making music in the time since it has been possible to issue recordings.
The first is that exemplified by classical artists, which is to utilise pre-existing pieces of music, written usually by other people (often long dead), and to become both exceptionally technically proficient at playing them and exceptionally expressive in interpreting them - such that one is able to combine one's own creativity with that of the original great genius who put the notes to paper.
Canadian pianist Glenn Gould would be a good example of this. Gould, like most classical musicians, devoted his career to playing pieces that had been written by other people (chiefly Bach and Beethoven) in order to use them as a vehicle for his own creativity. His recordings can therefore in most part be thought of as Gouldian elaborations or variations on pre-existing forms. When he was playing Bach, he was in effect using Bach's music to explore themes that he was interested in.
The most famous and controversial illustration of this may be his recording of Beethoven's 23rd Piano Sonata, the 'Appassionata', which is normally played at a quick tempo, but which Gould played almost absurdly slowly - thereby transforming it into an altogether different listening experience. (He did the opposite with the 2nd Sonata, 'Moonlight', which he played at an unusually high tempo.) Whereas in the hands of, say, Daniel Barenboim, the Appassionata's second movement is stately, grand, filled with saudade, but then exploding into joy, in the hands of Gould it is tentative, hesitant, contemplative, and finally melancholic. The same notes are being played, and in the right order, but to very different and distinct effect.
(On YouTube there is a recording of Leonard Bernstein, shortly to conduct Glenn Gould playing Brahms' Concerto No. 1 in D Minor, giving a speech to the audience in which he disclaims any responsibility for what follows.)
The important thing to note here is that the classical performer does not just 'play Beethoven'. He or she plays his or her interpretation of Beethoven. It is about putting one's own motifs, ideas, feelings and concepts into a familiar, accepted structure.
This can be compared with the approach taken in the world of pop music. Now, pop bands of course are known to play covers, and to play music written by other people. But since the 70s at least, the preference has increasingly turned towards newness. Yes, there is still the existence of form (some might even say formula) - verses, choruses, bridges, and so on - and still generally a recognisable pattern depending on the genre (the guitar four-piece, for example), and indeed genre itself imposes certain requirements. But all this is rather loose. The emphasis is really on creativity and innovation; the way to win status and admiration is to create new songs, not just rework old ones.
This is epitomised by the Beatles, obviously, who spent their (strikingly short) careers continually reinventing what they were doing - always writing new songs and always pushing beyond new musical frontiers. They are hardly alone in having done that, it goes without saying, but it is sometimes worth reflecting on the world of difference there is between a song written at the start of Paul McCartney's career ('Love Me Do', say) with one seven years later at the end of the Beatles' run (such as 'Golden Slumbers'). Here, the personal expressiveness comes not in the interpretation of pre-existing works, but in the creation of new works themselves - and indeed in re-interpreting the boundaries of what is thought possible within existing musical forms.
DMing styles are a lot like this. One the one hand there are the Glenn Goulds of the world. These are the people who dedicate themselves to the perfect technical execution of a particular campaign type (the megadungeon perhaps being the most obvious) and use the formal structure provided to channel their own personal creativity and ideas. And on the other there are the Paul McCartneys, who are always endlessly seeking to do new things - with their creativity being given much freer reign within a greatly looser set of parameters, ranging across genres, campaign styles and modes of play. Both are, needless to say, equally valid, and so is everything in between. Which are you? Gould or McCartney?