'Dutch' and 'Deutsch' have the same Germanic root, originally meaning something like 'people' or 'nation.' The word 'Dutch,' in English, originally referred to Germanic peoples more generally before narrowing to the people of the Netherlands because they had a lot more contact and rivalry with them. It's interesting to note that the Dutch call their language 'Nederlands,' and the German language 'Duits.'

fyi, while the following don't really go into the reasons that English speakers call people from the Netherlands "Dutch" rather than "Netherlanders", you'll find a bit more info on the origins of the term in these

• Why is the country Germany usually called something not even close to the native pronunciation, Deutschland? (Spanish - Alemania, Polish - Niemcy, French - Allemange) - see the last few comments at the bottom

• Why did the Germanic word France replace the Latin name Gaul, but the Latin name Germany survive against the German name Deutschland?

• Why does the english language call countries by names that are different than the names those countries bestow upon themselves? I.e. Germany - Deutchland, Spain - Espana, Austria - Osterreich, etc.