I'm a native Dutch speaker; and my job is one of the few where there is actually a difference between the two. So I hope this answers your question.
First of all, you're right in identifying that English and Dutch work the same way in this regard. For the purpose of staying on topic for English.SE, my answer only contains the English version; but you can assume that the same applies to Dutch.
I work at Google
You are telling me that the location of your work is Google (presumably headquarters, although any other official site of Google fits the description).
I work for Google
You are telling me that the work you perform is for Google. This doesn't inherently mean that you work at Google's headquarters (or any other official site of Google).
In the majority of cases, both apply at the same time. Most people work in the office/factory of their employer.
However, I'm a consultant. I work for MyCompany. ClientCompany1 signs a contract with MyCompany (temporarily hiring my services), and I go to ClientCompany1's offices to perform my job.
So for me, it would be correct to say:
I work for MyCompany; and I work at ClientCompany1.
Other examples could include:
I work for the Russian government as a spy, and I work at the NSA.
I work for Google, but I work at home (although "from home" is better in this specific case).
Whenever you say
I work at Google.
You are actually saying
I work at Google's office.
It doesn't have to be an office, it could be a factory, headquarters, a store franchise, ... This is either obvious from context, or irrelevant for the purpose of what you're trying to communicate.