Personally I don't like using stain. Reason being that a stain had relatively large particles of colouring (compared to a dye). When applied, these particles of colour tend to sit on the surface of the wood and then some other ingredient in the stain forms a barrier. This does the job of holding the coloured particles in place, but also prevents further colour from being added, it will just wipe off.
So with a stain you tend to only get one good go of getting the colour right, otherwise you have to strip it and start over.
With a wood dye, the colour particles are much smaller than in a stain, and they penetrate into the wood. Because they penetrate in, they don't need that covering layer to hold it all in place. This means you can add further dye and the colour will darken. So you can thin the dye out to like 10/90 and add the colour really slowly until you get what you want
I just thin with white spirit.
To get the look of that other stock, it might need some thinned down varnish, maybe multiple coats of danish oil. Good luck