The discussion on coat types, patterns and colors gets a little muddy depending upon what sources you trust.
The book, For the Love of Cats (by Amy Shojai and Irene Gizzi) defines it this way:
A cat with a coat that has some white in it is considered parti-color.
There are many variations of parti-color patterns, but the most common pattern in parti-colors is the bicolor.
The bicolor is two-thirds color (or pattern, such as tabby), and one-third white, or the inverse of that.
So, tuxies are bicolors (in this case, black and white), which is a type of parti-color coat pattern.
A black-over-white (one-third white) bicolor coat is your "typical" tuxedo. The black fur covers most of the back and the tail. They often have a white face with a black "mask" effect.
Some of them will have black spots on their faces, or a "goatee" effect of black on the chin. In addition, they have a white underbelly (chest and abdomen), and lower legs and paws.
Due to the association of tuxedos with formal occasions, some people say that tuxedo cats have "class."
Tuxedo Cats in Breeds
Different countries and registries define breed, color, and coat standards a little differently. The CFA, for example, has an interesting story of the history of parti-color Persians. This description doesn't mention any requirement, however, for white.
Some breeds are accepted in bicolor black and white by certain associations of the cat fancy. Many black and white cats are accepted for showing even if the pattern differs from that of a tuxedo pattern. Breed identity is defined by each registry, but some of the breeds accepted in black and white are the Manx, the Persian, the Norwegian Forest Cat, and the Maine Coon. Oriental cat breeds do not show in this color combination.
Famous Tuxedo Cats
First cat socks entered the White House when President Bill Clinton took office in 1993.
Sylvester, of Warner Brothers Looney Tunes fame. Sylvester has been chasing Tweety Bird since 1945.
Of course, he is always unsuccessful. This either makes him the most persistent cat in the world, or the worst hunter of the feline species, or both.
He may, however, actually be the most well known and famous tuxedo adorned kitty ever.
I first encountered the term "Jellicle cat" in the Andrew Lloyd Webber musical, CATS. CATS is based on T.S. Eliot's (much older) collection of poems, Old Possum's Book of Practical Cats. The musical, however, doesn't strictly follow the original work upon which it is based.
According to Eliot's poem, The Song of the Jellicles these cats are black and white, smallish, have cheerful faces, and pleasant voices. They rest during the day, and come out at night and dance under the Jellicle Moon at the Jellicle Ball. In Lord Webber's musical, however, the Jellicles are not strictly black and white, but exhibit a variety of coat patterns.