Each company has a culture whether it develops one consciously or not. You could say it's the soul of the company. It is something driven by core beliefs and principles of the company. Many companies claim to have values but how many of their personnel actually apply them in practice? Even that is a reflection of culture.
Culture describes how the organization behaves and how it reacts. It helps to describe how the company is structured and how it operates. It is something that unites the people of the company and makes them associate themselves with it. It is possible to end up with an accidental culture, especially in a startup context, if you don't take the meaning of culture seriously enough.
Cultures attract or abhor. This is the reason why culture fit is so important when recruiting. Even if you had someone who looks good on the paper, it doesn't mean the person will fit your culture. Perhaps your values are just too far apart and it won't work out. Learning skills is possible but changing your whole world view is a notch or two harder or even impossible.
To answer the original question, I would say it's impossible to separate a company from its culture. Different companies might have a similar culture but you simply cannot have a company without one. It is there regardless of how explicitly it has been codified in belief or principle statements. W. L. Gore's statement provides a nice example.
You could say culture is a crucial part of a company's DNA. This doesn't mean it cannot change, however. Semco is a very good example of a case where the culture had to change as a response to external threats to the organization. Some people had to go but the company remained and is doing well despite the challenges.