Here is a decent comparison of pigment (what he calls "dirt") and dye colorants.   I use a slightly different terminology in that anything that colors I call a stain and there are pigmented stains and dye stains.  One reason for that is that some of the canned products have both pigment and dye in them.

 

 

Here is another article on the subject (the "friend" is me).   I was doing a finishing class and could not find the chart that I had in one of my books classifying Minwax stains as pigment, dye, or both, and wanted to do a hand-out.

https://www.popularwoodworking.com/flexner-on-finishing-woodworking-blogs/is-there-pigment-or-dye-in-minwax-stains-does-it-matter/

 

My most recent Minwax experiment was their (new?)  "true black" stain.  It appears to be dye-based and comes out really black.

Good topic.  I bet this generates a lot of discussion.  It also prompts me to ask a question, prefaced with a somewhat long narrative explaining what I am attempting to do.  I recently scored a old style pitcher and wash basin at a local thrift store.  My plan is to build a display table to show off this buy.  I plan to make the table top from padauk, and put a 1/8" x 1/8" inlay strip, 1/8 " in from the edges.  I have a supply of hard maple left over from a Christmas project that I was going to cut 1/8" thick strips from, and dye them black.  Glue them in slightly proud of the surface of the table, and work them down flush to the top with a block plane, card scraper, or whatever would seem to work at the time.  I cut a test piece and applied the black dye.  When it was dry, I took my block plane and set it for a thin shaving to see how deep I had to go before I encountered white wood again.  One thin shaving, and the "scar" was white.  Okay, there is a reason hard maple is called HARD maple.  I repeated the test with a strip of poplar, and the results were the same.  I understand why the dye didn't penetrate the hard maple, but the poplar should have absorbed much more of the dye, right?  What am I not understanding?  I am now waiting to receive a $70 piece of ebony from ebay from which I can cut the strips I need, but why didn't the dye work, especially on the poplar?

As you can see in the video, "penetration" is a relative term.   Despite the thinness of the veneer, the dye only penetrated in the birdseyes, probably because of the direction of the grain at that very spot.  If you have ever tried to sand off blotched stain, you will also probably find it very uneven to get off, because of the grain direction.

 

Some finishes used to advertise some malarkey about "penetrates deep in the wood."  Ha.

It is my understanding that the only way to get penetration is under pressure. The color ply is the only wood I have ever seen with color penetration and even that is sometimes spotty. So I am thinking the thickness of the ply layers if the only reliable size to get color penetration. Now it may be possible with higher pressures and longer times than used for ply might yield a deeper penetration . However that would not be economically feasible.

1 hour ago, Gerald said:

It is my understanding that the only way to get penetration is under pressure.

 

True for wood but get that stuff on your skin and it is almost forever.  Gotta be through and through.  

21 hours ago, Gerald said:

It is my understanding that the only way to get penetration is under pressure. The color ply is the only wood I have ever seen with color penetration and even that is sometimes spotty. So I am thinking the thickness of the ply layers if the only reliable size to get color penetration. Now it may be possible with higher pressures and longer times than used for ply might yield a deeper penetration . However that would not be economically feasible.

Interesting.   One of the problems though is dye stains, typically in water or alcohol dry very quickly, so by the time you get air pressure up, or down and then released, I think you'd be too late, unless you are going to soak in the dye.