I can take a stab at it, but since there is not enough context this might be an educated guess as to the subject matter.

While a "trust" is a common law institution, it might still be a good translation depending on what your "stiftelse" actually does. If it is a way of separating assets from the owners in order to protect them from taxation, seizure, bankruptcy, divorce etc, then "trust" might be what you want.

It will all depend on the full context.

According to Merriam-Webster an institute is "an organization for the promotion of a cause"- This can be either non-profit of for profit. So if this organization was created to promote a cause, this is perhaps the most suitable word.

There is a very slim difference between non-profit and not-for-profit. For the IRS in the U.S., this is reduced to a few paragraphs of tax laws and a check box, differentiating nonprofit organizations and not-for-profit activities like reading a book.

In the business of business, non-profits and not-for-profits have different operating conditions. A non-profit can operate with no capital, never break even and still be a healthy organization. A not-for-profit organization needs to turn over the slightest of gains, a profit, to keep operating.

There is a number of other terms, such as agency and organization, on top of my own answer. The other answers are equally valid in this case, except for 'foundation', if we are talking about an organization registered in the U.S.

In your case, you will need to study the structure of the organization. Is it a single, consolidated organization, or is it a forum for other groups with shared interests?