A "house" is a building that you occupy as an inhabitant. It can also mean a building where people gather for social events (e.g. a movie house, houses of Congress).
"Housing" is a system where houses and flats are collectively referred to. For example, a government should have a sound housing policy to ensure that property prices are not beyond the reach of most citizens. "Housing" is often used to describe the prices (e.g. cheap housing), availability (e.g. shortage of affordable housing) or quality of houses (e.g. poor housing) in an area.
Other examples: A housing estate is made up of many houses. // The cost of housing in a city depends on the average prices of all houses.
Just as a side discussion, "house" can also be a verb which means to provide accommodation for people. Example: I cannot imagine how they managed to house twenty people in a rental flat.
Lastly, "housing" can also be a rigid and protective casing to contain parts of a machine or something delicate.
I hope this helps.