The steel wool is very fine and will actually scrape off a very fine layer leaving a silky smooth finish often referred to as a hand rubbed finish.
Sanding stain with steel wool.
Using steel wool or sand paper allows you to create a uniform surface for the next coat of polyurethane which generally looks nicer more professionally etc.
There is much info in previous q as here that touch on or directly answer some of your other queries e g.
Remove additional residue especially from difficult areas with a steel wool pad by scrubbing in the direction of the grain.
The use or not of wax variability of drying and curing times grit progressions should you choose to sand and polish.
Scrape directly into a trash can if possible.
Wipe all over the piece with 0000 steel wool using a light touch to remove any surface imperfections.
Steel wool can be used instead of fine sandpaper for many sanding jobs.
In addition it adds some tooth to the surface that helps the next coat of stain adhere and absorb better and more uniformly.
Step 9 brush on a third coat of polyurethane this time use it full strength without adding mineral spirits.
Wipe off the sanding dust with a tack cloth.
First it evens out the finish from the previous coat.
Before the stain remover has dried gently scrape the layer of stain and stripper residue from the wood surface with a plastic scraper or putty knife.
Then add distilled white vinegar to the jar.
You can modify this sanded surface subsequently by using steel wool with or without wax if it gives the look you like.
The very fine strands of steel gently cut into the surface being sanded removing an ultra thin layer.
Using steel wood to polish wood might seem out of place and actually harmful to the surface of the wood but it isn t if done properly.
The steel wool buffing process is fairly straightforward.
Sanding with a steel wool substitute between coats of stain is useful for two reasons.
In my experience assuming the finish is dry there isn t a difference other than the coarseness of the sand paper or steel wool.