In summary, an annex and an appendix are both forms of addendums to a main document. An appendix contains data that cannot be placed in the main document and has references in the original copy or file. An annex, on the other hand, is usually a standalone document that offers additional information than contained in the main document.
Looking at definitions, we get:
add as an extra or subordinate part, especially to a document
Annex is a term used more commonly in business models and ideas.
a section or table of subsidiary matter at the end of a book or document
Appendix is a term more commonly used in the research field.
An appendix cannot be submitted without the main copy. The aim of an appendix is to add greater details, visuals and examples for better understanding of the main copy. An annex, however, is different from an appendix in that it can be considered without the main text. It cannot be added to the main text but still has importance as regards the original copy.
Also, do note that appendices are usually written by original authors whereas annexes can be written by another party.
In this case, through the context given, I would assume you want the author to dissect the jargon and the business context in the design document, and since these information contains data that has references to the original copy and can hardly be used as a standalone document, I would suggest appendix.