Formal vs Informal

Ever wonder about the real difference between formal and informal language? I mean, the real difference? The real difference isn't that certain words are inherently more formal than others, it's that certain words are just generally accepted as more formal, even if the formal word and the informal word mean the same thing. Take the phrases "adhere to" and "stick to." One is far more formal and business-like than the other. However, when you really look into them, I mean really look into them, they mean exactly the same thing. Seriously, to "adhere" means to "stick." But in a business context, you'd never use "stick to" if you wanted to sound professional. You''d always use "adhere to." How and why did this happen?