All this train nomenclature in translation can be REALLY confusing. I'm going to make a plea to all the train advice-givers that we standardize our terms.
"DB, itself, refers to these as '"trains of the Bahn."'
OK, but I think it's a turn downhill if the Fernverkehrszüge/long-distance/high-speed trains should now be referred to as "Bahn trains." That only blurs the most important distinction IMO and doesn't de-confuse the confused.
"The Fernverkehr, on the other hand, runs the express trains (ICE/IC/EC) directly..."
I think of the ICE/IC/EC trains as "express" trains in English as well - but it's a bad label IMO for the German trains because of the Regionalexpress train (which then becomes an oxymoron!)
DB generally calls the non-ICE/IC/EC trains "regional trains" - as in...
Valid on all Deutsche Bahn regional trains (RE, IRE, RB, S-Bahn)
And DB generally calls the ICE/IC/EC etc. trains "long-distance trains" - as in...
The use of long-distance trains (e.g. ICE, IC, EC, City Night Line and
other international high-speed trains) is not permitted.
Since readers will be reading DB pages, I intend to drop my use of "high-speed trains" to refer to the ICE/ICE/EC etc. trains and to use the above terms consistently (to the extent of my skills at being consistent, anyway.)
Will you join me?