as far as i know, photoshop was the first to utilize layers and layering effects, and photoshop was first designed as a digital darkroom, rather than any sort of digital painting program. most of the layering effects, dodge, burn, pinlight, saturation, hue, etc. are references to techniques used in a darkroom.
layering also has its place in traditional painting media, especially acrylics, which dry quickly and are versatile in their transparency. but in painting, you are painting directly onto already applied paint, so the functionality of photoshop like layers is missing, ie. you can't toss out a layer and preserve what's painted underneath. different paint media act differently; oils for example, don't ever technically dry, so if you paint over something already painted, you'll pick up and blend into the color underneath.
there's also the technique of onion-skinning, used mostly in illustration, but it involves using trace paper to trace over in ink sketches done in pencil, to do line work etc. I actually think I remember past versions of Photoshop had a function called onionskin which pretty much acted as a layer.
i'm not familiar with Krita. My Wacom came with a version of Corel Painter, which does a pretty good job of replicating the look and feel of traditional media. For Evirea's portrait which I'm working on now, I'm trying out a combination of both programs.
I've seen other tutorials which are much more layer and effects heavy. The one I linked to used layers initially, but most of the work was done after flattening the image.
