Both the German and US/UK concepts of disability are specifically defined by statute and are therefore by their very nature not identical. They both certainly serve the same functional purpose and can therefore be used as perfectly adequate translations of one another.
There are multiple definitions - click on the translation that matches your context.
severe disability means:
an illness, injury, or condition that makes it difficult for someone to do the things that other people do
A £6m centre for people with learning disabilities has been opened on South Tyneside.
a disadvantage or handicap, particularly one imposed or recognized by the law
The suspension of his driving license, a major civil disability in his profession, resulted from his conviction for driving under the influence of alcohol.