There are differences, and they are not a problem in general …
Would not work, because switcher files need an installed OS to switch from.
Fairphone OS.
Anyway, if you really followed this guide faithfully, you should have had a phone running Fairphone OS 18.04.1. This should have worked for the new display.
For the new displays version numbers are important.
TWRP as well as Fairphone’s OSes require a minimal version number where support for the new displays was built in.
A new display will stay blue with official TWRP older than 3.1.1-1 or black with Fairphone OS or Fairphone Open OS older than probably 17.08.1. (I would suppose the TWRP included into Fairphone Open OS would work for the new display since probably 17.08.1, but I don’t know whether they followed the official version numbers with that).
That’s why the installation guide you linked to explicitly handles the case of a black display.
So, options:
You could install the latest official TWRP release, just follow the “Fastboot Install Method (No Root Required)” at twrp.me.
This should work.
You could follow the guide you linked to, but with the corresponding current “Manual installation” file for Fairphone Open OS (not OTA, not switcher) to get Fairphone Open OS on the phone even with a black display.
This should work.
You could have a look whether you happen to have fairphoneangels in your vicinity, who could perhaps check with another new display whether the problem is software or hardware.
You could contactsupport .