A wool tie sits in a different register from silk. Slightly more relaxed, much more textured, and much more at home with a sports jacket and odd trousers than with a formal business suit. The knot is the giveaway: square, with a bit of a dimple, in a cloth that has body to it, where a silk tie knots smooth and triangular. If you are wearing a tweedy or textured jacket, or you are going somewhere where a silk tie would look like you had tried too hard, a wool tie in a complementary colour is exactly the right answer.
Knitted and woven
There are two sorts. Knitted ties, made in a flat or ribbed knit with a square end, and woven ties, built like an ordinary necktie but in a worsted or flannel wool cloth. The knitted one is the more casual of the two, and the square end and the visible knit say so straight away. It belongs with a button-down collar and a tweed jacket. The woven wool tie is a little dressier and will pass in most business-casual offices without anybody blinking.
Colours run from the plain classics, burgundy, navy, forest green, brown, out to quiet textures and patterns in the same families. A wine-red knitted tie against a glen plaid jacket is a combination that has worked for eighty years and still does. A dark green woven wool with a charcoal flannel suit adds warmth without drawing any attention to itself, which is usually the point.