Looks like plaster to me - maybe not drywall???

It's definitely drywall. Maybe the lighting in this picture makes it look different.

I have patched a wall in my mother's basement that had this texture. I used a sponge dipped in Durabond 90. Durabond 90 is a powder that you mix with water, and it dries somewhat harder than regular drywall compound. I mixed it a bit drier than the instructions call for. I then dipped the sponge in the mix, and dabbed the wall with the sponge. The more compound you get on the sponge, the heavier the texture will be.

I recommend that you practice first on a piece of scrap drywall or cardboard before doing it on the wall.

@ksc36 where did you find that picture??

https://www.pinterest.com/pin/522839837973349278/

Roller with nap

Three roller applied textures

The key is getting the joint cement to the right consistency. Get a piece of cardboard or sheetrock. Start mixing a little water with the premixed joint cement. Roller it on your test piece - if it's to 'sharp', add a little more water.