Doctors use their own language when for the records - bokmål, nynorsk, danish ..

Each region has a main language (bokmål/nynorsk) and signs are in the corresponding language. For trivial signs like your example the text would be almost identical.

Bokmål is very close to Danish. Nynorsk was “constructed” based on dialects especially from the western parts of the country. Both bokmål and nynorsk are official written languages from 1885 onwards, people speak dialects, some closer to nynorsk and some to bokmål