What you are referring to, I believe is a plain text or a rich text Content Control.
You find these on the Developer Tab.

In older documents it may have been a Text FormField. These are also on the Developer Tab but I would recommend using the Content Controls instead. These are "legacy" formfields kept in the program for backward compatibility. Some people, mistakenly, refer to these as "text boxes."


The term "Text Box" in Word, refers to a graphical element, a box, in which text is typed outside of the regular document layer. These can be found under the Insert tab.

Resources:

• Create a Form Using Word Content Controls by Greg Maxey
• Repeating Data Using Document Property Content Controls and Other Mapped Content Controls
• Making Forms with Microsoft Word