"Authoring" versus "Writing"
Solution 1:
I would understood this subtle difference connotational-wise where authoring includes a higher level of creativity or other mental use. I would also say that all authoring is writing, but that not all writing is authoring.
Solution 2:
The verb author either means to write something (a book) or to create something (a computer program). I see no reason why one cannot use write for both purposes.
Solution 3:
Oxford Dictionaries Pro defines the verb author as ‘be the author of (a book or piece of writing)’ and ‘be the originator of’. The OED has similar definitions, with the earliest citation dated 1598. However, when author means ‘to be the author or originator of (a book, play, remark, etc.)’ it is described as ‘obsolete except in U.S. use’. As a BrEng speaker I would not use it as a verb at all, but if it is being used for a specific purpose in the computing industry, then so be it.