These usages are called "genitives." The genitive construction has many different meanings both in English and other languages. At a big picture level it modifies the head noun in a restrictive way, but the manner of this modification and restriction is very contextually dependent.
In your case the first:
The United States of America
Would be called a genitive of possession (the United States, which belongs to, or are within America),
The Kingdom of Cambodia
Is a genitive of apposition (the Kingdom, that is to say Cambodia.)
See the Wikipedia article on the genitive case.
One other point, there are two forms of genitive in English, the one you listed and the so called Saxon genitive, which uses an apostrophe 's. They have broadly similar meanings but are sometimes slightly different in emphasis.
America's United States
Means broadly the same, though the emphasis is on America here rather than on United States. (The meaning is also slightly obscured because "United States of America" is pretty idomatic, which is to say in some respects it is a semantic unit that should be taken as a whole rather than as a composition of its parts.)
Again conveys the same basic meaning, but has a subtly different emphais, as well as being subject to a broad idiomatic form for country names.