You are right about NDT but NDE means Non Destructive Evaluation in the industry I am currently employed anyway (Nuclear).
NDT detects and locates flaws, defects etc. while NDE goes more in depth with more precise location, shape, orientation and most important in the evaluation perhaps the longevity and useful wear rate of the piece.
seems rather due to the code or standard we use. ASME almost always refers to NDE (API too), while more AWS uses the term NDT. Both terms refer to the same.