A substance is “ferrous” if it contains iron.
Ferous is a suffix we use to mean “containing” or “bearing”; for example Carboniferous the era being named after the carbon bearing sediments laid at that time.
Is there any etymological relationship there or is that a coincidence?
This appears to be a coincidence. Ferous goes back to an Indo-European root *bʰer-. (“to carry”) while ferrous appears to go back to a Phoenician root (Semitic (non-IE) language).
And Ferris Bueller goes back even farther, to the inventor of the wheel.
Conifer, aquifer, transfer, circumference, differ, etc., etc. etc. –nothing to do with iron.
Latin ferrum, iron.
Latin ferre, to carry.
Coincidence. Like bear (carry) and bear (animal) in English.
My (ancient) Latin-English dictionary says, under ferrum: “cf. Sanscr. dharti, firmness; Lat. firmus”, so apparently some people at least imagined a connection.
Don’t forget about “feral” 
So iron-containing compounds (or geological layers) should be called “ferriferous”? 
In chemistry, the terms are explicitly and specifically defined.
“Ferrous” compounds have iron(II) cation Fe[sup]2+[/sup].
Compounds with iron(III) cation Fe[sup]3+[/sup] are “ferric” or have the prefix “ferri-”.
*Ferre *and firmus are from the Proto-Indo-European root **dher- *‘to hold’, which also gave us Sanskrit dharma.
But ferrum is traced < Phoenician *barzel *< Aramaic *parzela *< Akkadian *parzillu *< Ugaritic brdl, from Anatolian origin. Which makes sense, because iron smelting was invented by the Hittites, who spoke an Anatolian language.
However, the Hittite word for iron is hapalki, which instead may have become Greek chalyps ‘iron’, though that may have come from the Hittite word for steel, kikluba.
Thank you for the detailed responses. Etymology is fascinating!
It always strikes me just how similar Phonecian and Hebrew are.