In the testing field, the terms "published" and "unpublished" have special meanings when used in reference to measurement instruments. Instruments that are distributed by commercial publishers are said to be "published" (or "restricted") whereas those instruments available by other means, such as publication in journal articles, are "unpublished." This is a technical distinction but one that has bearings on the availability of instruments for study and use.
In general, published instruments (e.g., the California Psychological Inventory) are commercially distributed for a fee. They and companion materials such as manuals and forms typically are bundled together in a package for sale to qualified users. Under certain conditions, many publishers will sell an examination or preview kit but, as a precaution, such kits may not include all the items included in a complete kit.
Who is a "qualified user"? This depends upon the instrument. Publishers often code their materials in a fairly standard way (1,2,3 or A,B,C) to identify levels of qualified users. For example, see the Pearson Assessments web page titled Qualifications (https://www.pearsonassessments.com/professional-assessments/ordering/how-to-order/qualifications.html). Generally, the lowest level code (i.e., A or 1), provides the widest accessibility. The higher the level, the greater the restrictions on purchase. The obvious implication is that individuals who have identified an instrument for use in a project may discover that they cannot obtain the instrument--even to look at, much less to administer. This is a common plight among students.
This is the reason why "unpublished" instruments are used heavily by students. These materials often are printed in journal articles and reference books and may be readily available. The articles and books may include statements giving the permission of the copyright holder for the reproduction and further distribution of an instrument, requiring no other action on the researcher's part. Often, however, no statement regarding further reproduction and use is given. In still other cases, very explicit warnings are provided regarding such action. The catch is that even "unpublished" instruments are published in some sense. For example, a journal publisher probably holds the copyright for the journal article containing an instrument. The publisher may or may not hold the copyright for the instrument, depending upon its agreement with the author of the instrument (who may or may not be the author of the article!). In the latter two scenarios, reproduction for other than fair use purposes, and distribution of reproduced copies for the purpose of administration, are ethically questionable and may be copyright violations.
Here's the bottom line...Unless explicit permission is given in writing in the source publication, contact the copyright holder of an instrument to request permission to reproduce it--or modify it!--and use it in a study. Consent often will be given readily (particularly from individual authors), and the courtesy of having been asked will be appreciated. If you need help tracking down the appropriate person(s) for permission requests, contact a reference librarian for assistance.