These people are probably pretty close to what you think of as a "magic user". They use their mana to cast spells much as you would expect. They also look at magic in a sort of newagey kind of way—they're interested in crystals and magic artifacts (like amulets) and auras and lei lines and all of that nonsense. The fact that they insist on believing in that stuff is a major source of headaches for the more rationallyminded.
They annoy the shamans because they tend to misappropriate and distort the shamans' deeply held beliefs. They annoy the philosophers by borrowing some of the more scientific ideas (in order to appear more rational) and end up completely misapplying important tenets of modern philosophy.