The small one is a black Arkansas I bought at House of Blades in Lake Worth Texas nearly 30 years ago,back when they had a cougar that hung out in the shop.The big Arkansas came from Hand American and the lid has a leather strop glued to it that has green chromium oxide powder on it.
I have some DMT diamond stones for the harder steels,but for the carbon steels I prefer like O-1,1095cv,and Case CV,these old timey rocks work just fine.