As it turned out, both woods took the stain very well and I only had to apply slightly more to the second wood than I did to the walnut. I allowed the stains to dry for 72 hours for good measure before applying the finish, which was to be varnish. Varnish was chosen for two reasons. It is likely originally used on the chairs and I like the appearance it gives to the wood. In my opinion, polyurethane makes the furniture look like it has been coated in plastic, a problem not found with varnish or shellac.
Varnish comes in various sheens or degrees of brilliance from a matte to high gloss.
These terms basically refer to how much the piece with shine when dry. The dullest finish most commonly found is matte, followed by satin, then gloss, and then high gloss, the shiniest of all. Several years ago I found and have developed a fondness for an eggshell finish which is between matte and satin in terms of shininess. It has a hand-rubbed look to it which also looks like it has been on the piece for a while. In other words, it looks very nice but doesn't necessarily look brand new.