Exact difference between demi glace and bordelaise? This feels like a stupid question, but I've spend a fair bit of time reading about this without finding an answer...
I'm trying to understand the French mother sauces and their derived sauces. I am confused about the differences between demi glace and bordelaise, their place in the 'system', and whether roux is used in either.

Reading about espagnole here, I learn that espagnole


Starts with a brown roux, and
Can be used to make demi glace AND bordelaise.


This confuses me, because I've encountered recipes for either, which have not mentioned roux. For example, this demi glace recipe by ChefSteps makes no mention of flour or roux - only reduced wine and stock.

Similarly, this bordelaise recipe, for instance, is virtually identical (except for adding butter towards the end).

Hence, I'd be grateful if anyone could help me understand


Precisely what is the difference between demi glace and bordelaise?
Is roux used in either? If not, how can they be derived from sauce espagnole?
Demi glace is usually used as a base to make other sauces, it can also be used by itself.

Demi glace is used to make Bordelaise sauce.

Roux is not used in either cases.