Formal (Morning coat and white tie) or semi-formal (black tie) dress is best worn in tandem with a formal overcoat. And formal overcoats do exist or at least they did exist. Take a look at films from the 1930s and you will see the black SB coats often assorted with capes. The cape is probably the last remaining vestige of formal outerwear that exists today.
Emily Post's 1922 advice is still applicable and up to date:
"When you go out on the street, wear an English silk hat, not one of the taper crowned variety popular in the “movies.” And wear it on your head, not on the back of your neck. Have your overcoat of plain black or dark blue material, for you must wear an overcoat with full dress even in summer. Use a plain white or black and white muffler. Colored ones are impossible. Wear white buckskin gloves if you can afford them; otherwise gray or khaki doeskin, and leave them in your overcoat pocket. Your stick should be of plain Malacca or other wood, with either a crooked or straight handle. The only ornamentation allowable is a plain silver or gold band, or top; but perfectly plain is best form." (http://www.bartleby.com/95/34.html)
Formal overcoats, worn rarely, and crafted from heavy black cloth tended to last generations. So look in your grandfather’s collection and see if one is there for you. If your granddad wasn’t much of a dandy, you might try vintage clothes stores. It used to be you could find lovely examples in London and Paris flea markets. But that was 35 years ago.
As far as matching overcoats and semi-formal wear there is a bit more latitude. But wearing covert coats and Barbour jackets with DJs is a real shame.
Black silk top hats are de rigeur for formal wear and would be wonderful to see again. The black Homburg should be used with semi-formal dress and city suits. The rules used to be that a Homburg can only be worn in Black. As a matter of fact, the hat merchant Bates in London, only sells black Homburgs for this reason. There are some notable exceptions thanks to some notorious rule breakers:

The “Coke”, aka Bowler or Derby, was invented in 1850 at the request of a gentleman farmer Mr. Billy Coke who wanted a hat that would protect the heads of his game-keepers from low hanging branches. James Lock and Co. made the first model and the story goes that Mr. Coke jumped from a chair onto the hat and when it did not budge under his weight he accepted it. The hat, designed for country wear, made its way into the city worn by a true mish-mash of clients from bankers to Irish Protestant loyalists to military officers. It was never considered a hat for Formalwear in England, at least. Hardy Amies once wrote about the dreadful thing “It should never be worn on foreign soil, never worn by foreigners and Americans who wear one should be sued!”
The discussions in this thread highlight the importance of building a consistent sartorial lexicon. By using terms that have been clearly defined we do better service to those who visit these pages to learn or gain new insights.
In Europe one tends to break down dress by city clothes and country clothes; and eveningwear versus daywear. So one might refer to “Formal, City and Country” as categories of dress; and “Evening and Daywear” as subs of each.
The concept of “dressy” or “formal” or gradients of “dressiness” seems a bit vague since one is supposed to be well dressed at all times. And the use of the word “formal” as a synonym to “dressy” does create confusion with Formal with a capital “F” (see Manton’s distinction above.)
“Formal” describes a specific category of dress. Semi-formal, as pointed out above, is a sub of Formal.
City eveningwear describes the kinds of city suits most appropriate for wear after nightfall, to restaurants, clubs, for a walk in the park. City daywear indicates the kind of suits best worn in the city for work purposes, or for living a life of leisure (God willing!)
It is hard to breakdown Country wear into Evening and Day use. So that leaves us with the following:
Formal
Evening and Daywear
City
Evening and Daywear
Country
This subject will be developed in its own thread, upcoming.
Cheers