Historically, examiners have used the term ‘authorship’ when referring to the issue of who produced a questioned writing.  More recently, the term ‘writership’ has appeared in the literature.  One example is the Forensic Handwriting Examination and Human Factors: Improving the Practice Through a Systems Approach document (aka, the HFHE report; see this link and this link).

This is a point of contention insofar as forensic handwriting  examiners address questions regarding the person who wrote a given sample of writing or a signature.  Still, the distinction between the two terms may not be obvious, which is its own issue. 

This is how the authors of the HFHE report explained their choice of terminology:

The term “author” often refers to the creator of the content of a writing. Thus, studies have examined who composed the specific essays in The Federalist Papers (Hamilton, A., J. Madison, and J. Jay. 1788. The Federalist. A Collection of Essays Written in Favour of the New Constitution as Agreed Upon by the Federal Convention, September 17, 1787.) that appeared under the pseudonym of “Publius” and who wrote the works attributed to Shakespeare.  “Authorship” in that sense is the subject of forensic linguistics (see, for example, Zheng R., Y. Qin, Z. Huang, and H. Chen. 2003. “Authorship Analysis in Cybercrime Investigation.” In Intelligence and Security Informatics, edited by H. Chen, R. Miranda, D.D. Zeng, C. Demchak, J. Schroeder, and T. Madhusudan. International Conference on Intelligence and Security Informatics (ISI) 2003. Lecture Notes in Computer Science 2665. Springer, Berlin, Heidelberg.)  As the writer of a physical text might not have been the original author, the Working Group uses the more precise term “writership” throughout this report, rather than the broader term “authorship,” to denote the physical executor of the handwriting under examination.

On the one hand, this argument is reasonable.  The term ‘writership’ may be more precise.

On the other hand, I think that few people are confused by the term ‘authorship’ when used to mean the actual person who physically wrote an entry. Those same people are unlikely to recognize the term ‘writership’; thus creating a potential source of confusion and, at a minimum, requiring explanation.

Hence, most examiners still use ‘authorship’ and see little need to change despite the potentially greater precision of the term ‘writership’.  I personally switch between the two depending on my audience and their preference.  I have no issue which word someone chooses to use so long as the underlying issue is clearly understood.