I am not a native speaker of English. In http://www.grammar-monster.com/easily_confused/comprise_comp... the difference is:

Make sure you name all the constituent parts when using comprise or compose. The word to use when other elements are may also be present is include.

The elements one, two, and three composed the set {1,2,3}. The set {1,2,3} is comprised of three elements. The set {1,2,3,4} includes the elements one, two and three.

In http://www.thefreedictionary.com/include all this is clarified, the botton line or golden rule of usage (edited).

  Some writers insist that include be used only when it is followed by a partial list of the contend of the reference of the subject. This restriction is too strong. The use of comprise or consist of  will avoid ambiguity when a listing is meant to be exhaustive.

I agree that it's the opposite of standard usage but that's how it's interpreted in patent language. Here's a quote straight from the USPTO website:

"The transitional term “comprising”, which is synonymous with “including,” “containing,” or “characterized by,” is inclusive or open-ended and does not exclude additional, unrecited elements or method steps." http://www.uspto.gov/web/offices/pac/mpep/s2111.html

There are other non-standard interpretations in patent language. For example, "a" or "an" is not necessarily a singular but can mean "one or more". Also the inventor is free to provide their own definitions for words they use in the patent specification.

That definition of "comprise" is more or less the opposite of the British English definition, where "A comprises B, C and D" means "A includes B, C and D and nothing else." E.g Parliament comprises the House of Commons, the House of Lords and the Queen.

I agree. It confused me when I first started looking at patents but the accepted usage in patent law is that it is open-ended and can include other non-mentioned elements.

That's what I thought initially when I encountered the word, but there were judges ruled in patent cases where "comprise" means the items making up the entire parent item, no more no less.

Do you remember the specific cases? I'd be interested in knowing the details of these rulings. If you look at the Garrod Glossaries you'll find several examples of the "open-ended" claim construction for comprising.