In addition to being tightly twisted, worsted yarns for weaving have been straightened, and traditionally use longer-staple fiber, which helps achieve the smooth, tight, uncrimped yarn that is the hallmark of worsted.
Woolen yarn is spun out of wool with still-crimpy fibers running anyhow, which prevents the smooth finish and tight twisting of a worsted. The resulting yarn is fluffier and has little ends poking out.
Because of these properties, worsted fabrics generally wear better (the smooth finish prevents pilling and felting) and look neater (again, the smooth finish resists lint, hair, and stains) and can be woven into very lightweight fabrics because the yarns can be spun more finely.
Woolen fabrics are warmer, because the crimp in the wool and the looser spin trap more air. They also are thicker and fluffier for the same weight of goods, again because of the looser spin. And they resist creasing, because the natural crimp of the wool and the multidirectional fibers won't get organized and lie down in the same direction.
Worsteds and woolens both come in a variety of weights. Tropical wools are usually worsted, made from tighly spun yarn that is woven more loosely to allow airflow. When a seller just says "worsted fabric" they're probably referring to a pant-and-jacket weight, but check for any modifiers. Very high-quality, middleweight suitings are made from extra high-twist worsted yarn; these are twisted tighter even than usual for worsteds, making a very strong, long-wearing material with a very smooth finish. Normal twists are in the 60-80 range; when you see suiting labelled as "super 110" or "super 120," they're referring to that extra twisting.
Fabrics in which woolen yarn is most used include tweeds, flannels, and soft coatings.
As far as what to look for when shopping for dress and jacket fabrics, unfortunately modern seller s do not label their fabrics for mid-century uses! Because of the layering and sheer volume of fabric in a mid-century dress, lighter is generally better, but "tropical" and "lightweight" will both work. For jackets and even mantles, you still want to think thin - generally no heavier than suiting weight. If you need it to be warmer, rather than going up to a coating weight, instead add layers - a silk lining, a flannel interlining, and/or thin wool batting will add a tremendous amount of warmth.