An SUV refers to a Suburban Utility Vehicle. This may or may not be equipped with 4 wheel drive. It is also usually an enclosed, multi-seated vehicle. Basically a glorified station wagon. A 4X4 is any vehicle that has 4 wheel drive. Usually it is thought of as an open bed truck with 4 wheel drive.
In the UK SUV means 'Sports Utility Vehicle'. It is regarded as a modern more hip version of the traditional 4X4 (Land rover/Range rover/ Jeep etc.). SUV's are designed for road use and the 4X4 function on them is not that good for off road use - if you want something for that you are better off looking at traditional 4X4's.
4x4 refers to 4-wheel drive and is available on SUVs and on trucks and probably on other vehicles too.
SUVs are available as 4x4s or with 2-wheel drive.
Added material: SUV & 4x4 are arbitrary labels of function with may overlap. It's like "spinster" and "mother", which may be presumed to be two different categories, but, when used precisely, rather than loosely, have some intersection. There *are* mothers who spin with wheels or with drop spindles.
In some USA areas a SUV is commonly thought of as a Suburban Utility Vehicle and is what can be used to haul people or a refrigerator in enclosed fashion.
