All of the above can be used. Depends on what the job is,,the wood,, the repair if any. What finish is already on the wood, what is going over it. .
Stain can be used especially solvent based stains to enhance grain and add to it.
A repair in the wood will usually still show with the use of just a stain. It's just natural that the different piece of wood and any glue line no matter how careful the repair will accept any stain differently than the base wood around it.
Color in the finish, toned finish I guess it called, works very well in some instances where the colors co-operate with you.
Paint can be used but the application is the key. Very light coats,,an air brush is often used to advantage and it's ability to feather the edges of the color layers is not to be overlooked.
Brush application techniques are something to be learned along with the ultra thin coats.
I've settled on using acrylic paints. They dry fast and can be applied so thin that one will show thru others to create the needed look.
It's not just a couple of colors mixed and applied and that's it.
When completed, the color repair needs to be 'fixed' with a durable transparent overcoating. This can be toned with a colorant as well to comply with the final finish if needed..
Then the real finish is applied over than to match the rest of the stock. Or perhaps the entire stock is being refinished along with the repair(s).
Here's Win21 that needed the stock refinished but had a missing piece of wood by the frame.
The orig repair was a glob of fiberglas.
I fitted a new piece of walnut and fiberglassed it into place. Fitted close but the 'glass still shows at a couple spots along the glue lines.
No matter, the epoxy is strong and hard and won't flex like a resin glue line so the repair won't show.
The wood doesn't need to match in color or grain as it is being sealed over first,,then painted to mimic the color and grain of the orig wood,,then 'fixed' with another sealer,,then the final finish.
The slight foggy look to the repair is the final coloring done, but no fix applied. That will brighten and match the color area with the rest of the surrounding wood. Then the final finish applied to the entire stock/
That final look I unfortunately can not find the pic of. But you can get the idea I think.
This is only one way to do this.
Like most everything else in this business,,there are many ways to the end result. Techniques vary and what ever works for you to get those results is the path to take.
It takes a lot of experimentation, time & effort,,, failed efforts.
Stock with a repair piece epoxied into place, shaped and sanded. I think I had applied a sealer at this point.
Building up the color and the look of the grain with the acrylic paint. Brush techniques are used to get the right looks. No Airbrush used, just cheap artists brushes. I clip them to different shapes and lengths to give different effects.
Coloring (painting) pretty much completed. It gets a very light going over with 0000 steel wool after a complete drying for a day or so.
That will blend the edges of the coloring into the natural wood grain/uncolored areas well.
Then the very light coating of 'fixer'.
I apply that with a brush.
It can be anything from thinned shellac (orange or white) to a wiping varnish, ect.
Something that drys hard and fairly quick. Nothing with a linseed oil in it as I have found that will start to soften the acrylic colors, mix and blurr them.
It can be used over the fixed coating however as the colors are then protected.
Well that's the way I fix up repairs in wood. But like I said there's lots of ways to do it and results are what count.
There are some artists that can make a piece of appliance crate wood look like a blank of English thats suitable for a Purdey.