Ayy, hello there, fellow German.

So, first of all, English generally does make the disctinction between "Germanic tribes" and the "German people". You wouldn't refer to the modern Germans as Germanics, nor would you call the Suebi or Alemanni German tribes, but Germanic tribes instead. Dan Carlin not making this distinction is a Dan Carlin problem, not an English language problem - whether he made the choice you describe out of ignorance or simplicity I cannot say, but the English language certainly has the distinction you describe.

Now, onto the history and lingustics and lingustic history, then.

The German demonym "Deutsch" is derived from diutisc, a Germanic word meaning something like "part of the people" or, effectively, "part of our people".

However, the concept of a German people is actually rather young. The concepts of German peoplehood and German language came around in the late first millennium. The first "German" "state" in turn was East Francia, that at that point might have already been referred to as a Diutsch or Teutsch part of the former Frankish realm, a "German Land", or 'Deutsch Land'.

That is not even to speak of the concept of German "nationhood". Nationalism and the desire for a common German nation state wouldn't be around for another 800 years even at that point. Referring to oneself as German became popular over the course of the second millennium, but only the enlightenment and especially Napoleon with his at that point more advanced humanistic-liberal model brought the idea to Germany - even if that process of bringing the idea to Germany was done through hundreds of cities surrendering to the French and being put under French administrations. That of course then led to the 1817 and 1832 festivals, to the 1848 revolution which was struck down, and then, in a power grab that I personally view as 'Greater Prussia' much more than it was a 'Germany', to the unification wars of 1864 through 1870 and eventually to the unification of the German Empire, Germany's first true nation state.

So, once more back from history to linguistics. As I have already shown, the German word "Deutsch" comes from Old German. Where does the English word "German"/"Germanic" and the German word "Germanen" come from? Well, immediately from Latin's Germani. We don't know whether the Romans took that word from the Greeks or even from the barbarians they were naming, be they Celtic or Germanic or whatever, but we know that the Romans used that term.

And that, when viewing history, gives the German language enough a reason to draw the distinction between "Deutsch", which as a concept likely wasn't around at least until Charlemagne, and "Germanisch", which was the term for the German people's ancestors during the Roman times and before.

So why does the English language use "Germanic" as the ancestor word for "German" instead of being so nice to copy our glorious "Deutsch"? Well, we have our lovely bikeriding cheesemaking windmillbuilding neighbors to the northwest to thank for that one - because the English did use some form of the word 'Deutsch' in their language, but as the northwestern German area, the one that was always trying to steal English colonies and spices and that was so uncomfortably close to Britain, developed into a distinctly non-German people, that people kept the word for themselves - the Dutch. This is an anomaly, as the Dutch refer to themselves as "Nederlanders", the Germans call them "Niederländer", the French choose "Néerlandais", but only the English language chooses 'Dutch' instead. The English word 'Netherlander' also exists, but is in practice almost never used - you would instead use 'Dutchman/-woman'. It would appear more normal to call the Germans Dutch or Deutch and the people from the Netherlands Netherlanders - but logic does rarely dictate linguistics, as a language's development is a vivid process that is observed and advanced by faulty humans leading to apparently faulty languages. And that's a lovable quirk about them.

Silly Dutchies, stealing our words.