Trim and Finishes

Base Trim and Door Trim and Window Trim can (and are) all called trim. Also known as Baseboard (or Base Molding), and Door and Window Casing.

Finishes are simple varnish (3 coats with a light sanding inbetween each coat.)

More elaborate finishes would include a sanding sealer as the first coat, followed by 2-3 additional coats of varnish.

Varnish is an oil based material that will "amber" over time.
Polyurethane can be/is either a chemical based or a water based product that doesn't "age" the same as varnish.
You can put polyurethane on top of varnish but you cannot put varnish on top of polyurethane.

Staining wood enhances its already beautiful graining. Wipe on, Wipe off.

Gell finishes allow you to be more creative, especially when needing to match older wood finishes.

Painted wood trim always has an elegant look. Oil-based paints are slowly being worked out of the market. Latex is all that will be available in the forseeable future (no telling what a chemist will develop.) Latex is an acceptable (though not quite as lush) alternative option to oill-based paint.