As adjectives the difference between familiar and known is that familiar is known to one while known is someone or something that many people know about, renowned, famous. As nouns the difference between familiar and known is that familiar is (obsolete) a member of one's family or household while known is in algebra, a variable or constant whose value is already determined. (This is from google) When I first thought about it, I came up with this. Familiar with is something that you're not 100% sure about or something you might not be confident that you know about. Do you know Martin Scorsese's work? I'm familiar with Martin Scorsese's work. (You know it but you're not confident it's the right person you're thinking about or that you know all of his work) Know is something that you're 100% about or know well. Do you know answer number one? Yes, I know answer number one. (100% or confident about it)

Ok i have a coment about you i study structure I'm going to the restaurant to pick up our orders She's holding three cups of coffe I holding a pitcher between my hands

To be familiar with= very comfortable with, used to, to have an established relationship. Familiarity eg Im familiar with this city as I live/ have lived here. To know= to understand, to have knowledge. eg I know how to go from the East to the West end of the city.