Obviously we all have our history and folklore. here is mine...
means red as in red fox or red head colour i.e. red-orange-copper. A male red head in French is called un Roux
and a female, une Rousse,
the feminine colour is also used to describe an amber beer.
A typical roux is used for brown to dark coloured sauces whereas, as you all know, you add fat + flour and let is react until it colours...
there is 3 food science principles at play here:
1- Fat and starch don't mix. When both are combined and heated the fat separates (disperses) the starch granules so that they won't clump together when hydrated with water. (as @Someday
alluded to in his explanation)
2- Warm fat coated starch granules soak up water slowly and uniformly so that the addition of water can be controlled (i.e. thick or loose). Adding warm liquids to dry flour always clumps (unless excessive mixing is involved) Risotto making works mainly on this principle. When starch granules are left to soak in water only, the granules swell but also bust which breaksdown the thickning potential. It become glue like and runny.
3- Since fat can attain higher temperatures than water, fat coated starch granules first harden (to help principle 2) then can brown with the protein in the flour (Maillard reaction). The thickening power of the roux, decreases as the colour increases but more colour means more taste (umami). I'm guessing here but, probably a roux (rust red) colour is the best combination of flavour and thickening when initially developed by a French cook to make and describe his recipes.
the difference between using fat or butter lies in the fact that butter has 10% water content. If the water is not driven out of the butter correctly then it will pre-gelatinize the flour and reduce it's thickening potential because the granules will breakdown prematurely. When using butter, it would be preferable to heat the butter first until it foams (water released by steam) then add the flour followed by cooking to the desired colour.
Note: the Maillard reaction is a chain reaction meaning once it starts the colour development cascades quickly. Controlling heat is your friend. I have indeed been able to attain an actual roux (copper penny like) colour with butter and flour on moderate heat and plenty of time. Like making caramel with melted sugar.