A term I hear now and then is a "CUA" text editor.
What is a CUA editor?
According to Wikipedia, CUA is...
Common User Access (CUA) is a standard for user interfaces to operating systems and computer programs. It was developed by IBM and first published in 1987 as part of their Systems Application Architecture. Used originally in the OS/MVS, VM/CMS, OS/400, OS/2 and Microsoft Windows operating systems, parts of the CUA standard are now implemented in programs for other operating systems, including variants of Unix. It is also used by Java AWT and Swing.
In other words, a set of a standards/guidelines for interactive applications to follow.
To more specifically answer the question, a CUA editor would then simply be a text-editor which adheres to the standards/guidelines set by the CUA.