There is no essential difference. proficiency level......... Adjective+noun level of proficiency .......
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There is no hard rule. All of the examples you provided are good grammar (in the US).
1. Both forms are commonly used for departments, for example, with no obvious grammatical change to the nouns.
- US Commerce Department; US Department of Commerce
In other cases, the use of an adjective is obvious.
- The German Chancellor; the Chancellor of Germany