There is a saying that has grown in use in recent times: “Any man can be a father, but it takes someone special to be a dad”. Put bluntly, it is a very silly saying. The saying is predicated on the notion that being a dad means one is more involved in the every day life of a child. In reality, there is no difference between those two words, as they are both just words to describe the same thing. None. Zero. The two words actually mean the same thing.
The distinction between the two words is that they are often used by two different classes of people.
If you belong to the highest class of people where proper etiquette and grooming are imbibed into children from the get go, your kids will most likely address you as father or mother. Everyone else outside of that class (meaning the rest of us) usually have their kids call them dad or mom. It has nothing to do with the level of involvement or intimacy between the father and child. There is a finesse involved in a child using the word father instead of dad, and it is that level of finesse that I would love to see in my kids.
Next time someone tells you any man can be a father, but it takes a special someone to be called dad, the joke is on them. They have no idea what they are talking about. If at all we have to make a distinction, any man can be a dad; only among the cream of the crop will you find a father.