"Clean" typically means something is not dirty; a pair of shoes with mud on them is not clean. You would not, however, say the shoes are "not tidy."
"Tidy" typically refers to the organizational state of things. If someone's house is "tidy," it is well-organized.
When talking about houses/homes in specific, though, people usually associate "clean" and "tidy," so it can be confusing. You could have a house that doesn't have any dirt, mud, trash, or old food in it at all, but it could still be considered "not tidy," and by extension "not clean," if you had stuff piled everywhere and it was hard to walk in the house because of it.