Macbook pro showing "Starting Internet Recovery" instead of AHT
From Apple's documentation on AHT:


  Some Macintosh computers that shipped with OS X Lion and later support
  the use of Apple Hardware Test over the Internet. These computers will
  start up to an Internet-based version of AHT if the hard drive does
  not contain AHT.  An Internet-enabled connection via Ethernet or Wi-Fi
  is required to use this feature. Internet-based AHT functions the same
  as AHT on the hard drive or flash storage outlined above.


What you are using is AHT, it just doesn't have it pre-installed on your hard drive.

EDIT:
You should have the option to perform extended tests, it will be a checkbox you have the option of selecting before running the tests

EDIT 2:
As your mac was made after 2013, you are forced to use Apple Diagnostics, which is why I assume you can't have access to the extended test options you see on the AHT documentation.