Simcha, it doesn’t really matter how it became this way. The fact is that it is this way today. Changes happen gradually and there is little value inherent in the specific clothing, but the point is that we have our own clothing, which was always considered a good thing.
I can’t promise you that we always dressed so differently. In fact, it seems that at times it was pretty easy to confuse a Jew for a non-Jew. Very often the differences were subtle. But there was always a point to dress Jewish. Today, there is no universal dress code for all Orthodox Jews, but to those that have it, it’s real.