'Everyday' is not a word I would apply to either of these words. 'Refuge' is a word that is commonly used for a place of safety, for example a place that provides accommodation for women who are being beaten up at home.
'Sanctuary' is the mediaeval right to escape from the law in a church. Hence it is sometimes used as a home for lost and unwanted animals: for example there is a Donkey Sanctuary in Dorset. Oh, and 'sanctuary' can mean a sacred place, and so the street outside Westminster Abbey is still called 'Broad Sanctuary'.
I guess all sanctuaries are safe havens. Even in the definition of a sanctuary as part of the alter or a church or a sanctuary as a reservation to protect wildlife. I would say sanctuary or shelter are more common than safe haven.
"Safe haven" (usually 2 words) is usually more literary - in addition to se16teddy, it could also refer to refugees seeking protection. "Sanctuary" could also refer to someplace that is considered to be holy such as a church, temple, mosque, etc.
I would agree with se16teddy that they are not everyday words - and I'd go further and say that 'safehaven' is not a word at all, it is used as two words - "safe haven" and I would see it either as a nautical expression, or as archaic. My main contact with the word "sanctuary" was with the main altar area of Roman Catholic churches - that was always referred to as "the sanctuary" when I was young. There are a few wild-life sanctuaries but I think the word "reserve" is beginning to come into vogue for those.