The ones I've seen were both, kinda. I've seen a number of horns where the plugs were painted, and where the paint was gone, there was some underlying stain. After a bit of work, I'm pretty sure they were done with oil paints. The difference in whether there is "staining" left behind may be due to the use or non-use of a primer.
To duplicate the red w/stain, for example, I made oil paint by mixing 50 ml of stand oil (I used Williamsburg Stand Oil from Dick Blick) with 25 ml of turpentine, then stirring in 11 grams of powdered red ochre.
This is a fairly "glossy" paint. You can matte it out by increasing the amount of ochre--but go slowly and experiment often. In small quantities, it is easy to go too far. Pretty soon, you find yourself adding a little oil, then a little turpentine, then a little more ochre. . . then you find yourself looking around for a barn to paint.
Applied to some pieces of wood and dried in the sun, the recipe given did a decent job of duplicating the period paints. Then I got brutal, and removed it with a heat gun and scraper. The pigment/oil remaining in the wood looked like the red stain you mentioned.
If you want just the paint effect, with bare wood showing when the paint wears off, prime the wood before painting. I've used a primer made of equal parts by volume of stand oil and turpentine. Let it dry before applying the paint.
I experimented with red ochre for reds, yellow ochre for yellows, and verdigris (copper acetate) for greens. White lead for white. I never tried for a blue--if replicating something post-1815 or so, you might try adding cobalt blue oil paint to the stand oil/turpentine mixture. Don't forget that verdigris oil paints will go on blue-green, but aren't stable until they age to a dark green.
That might be enough to get you started. Just a friendly warning: if you use a heat gun to strip back some of the paint, do it OUTSIDE. Trust me on this one!
Jim