No musical instrument illustrates the yearning gap between classical music and traditional music like the four-stringed wooden box I've been playing for the last 13 years. It starts with the name. Ask me what I play, and I would tell you I play the fiddle; ask a classical musician what it is I play and he would say "violin". But really, it's the same instrument. (Admittedly, this only applies to English - the Dutch call it viool, no matter how you play it.) I sometimes meet violinists (that is, classically trained musicians) who approach traditional music as a simple sort of classical music - a subset of classic, to use a mathematical term. If you can play Paganini's works, sure you can play The Maid Behind The Bar, right?
Wrong. They're totally different paradigms. Different worlds. It's almost like you're playing a different instrument. And let me be blunt: a classical training is a serious impediment to playing traditional music.
It starts with the fact that we know the composers of almost all compositions in classical music, but most tunes in traditional music have composer "unknown". The composer of a classical piece still owns it, as it were. Change the notes and it's not the same piece anymore; even worse, it would be disrespectful, like painting a mustache on the Mona Lisa. Yes, classical musicians interpret the music they play in their own way, through the intonation and the dynamic they (or the conductor) choose. But they must stick to the written music. On the other hand, apart from recent compositions, traditional music is public property. In fact, part of the fun of playing traditional music is the freedom of interpretation: let's put in some more syncopation by playing these notes a bit differently... Did you know that this tune sounds great when you play it in a minor scale? If I bind those notes and skip these it sounds really great on the fiddle. Also, there are often many versions around of the same tune.
Second, traditional music was originally developed to accompany dancers, so the most important element of it, high above the rest, is the rhythm. You can be a virtuoso all you like, it don't mean a thing if it ain't got that swing. Classical music, on the other hand, remains a work of art, strongly associated with the composer. So all facets, including melody, harmony, and arrangement, are to be appreciated, and rhythm is usually not the most important part of it.
Third, a classical training starts with reading music, whereas a good workshop in traditional music teaches the tune by ear. Let me be even clearer on this. I know a musician who took classical music lessons as a kid and she told me her father would slap her if she gave only the slightest hint of playing by memory rather than from sheet music. On the other hand, in most fiddle workshops people have recorders with them (mobile phones, nowadays), and the teacher distributes sheet music only at the end of the workshop, if at all.
This will sound mean to you if you are a classical musician, but every now and again I meet violinists who cannot learn a tune by ear, and even if they know the tune they still cannot play it by heart. Like barrel organs, they're lost without their sheet music.
So kids, when you want to learn to play music, stop reading it.