The set
A standard Western set is built from the faces of a pair of dice, plus blanks.
European dominoes are rectangles that are twice as long as they are wide. There is a single tile for each combination of the faces of a pair of dice; the blank suit is the throws of a single die, for a total of twenty-eight tiles in the standard double-six set. pagat.com The set contains 28 tiles, one from each pairing of the numbers 0 to 6. pagat.com Britannica Kids says the usual set consists of 28 dominoes: flat, rectangular blocks made of bone, wood, or plastic. The 28th piece is the double blank. Britannica Kids
The double-nine set of 55 tiles, containing all possible pairs of numbers from 0 to 9, has been around since the early 20th century at least. pagat.com Larger sets have become popular for some North American games, notably Mexican Train, which uses a double-twelve set of 91 tiles. Double-15 sets (136 tiles) and even double-18 sets (190 tiles) can also be found. pagat.com Other sets with larger numbers of tiles were invented later, with the double nine and double twelve sets being the most common extensions, in Pagat's history wording. pagat.com
A different set
On a Chinese set the ends show spots from 1 to 6, corresponding to the throws of two six-sided dice. There are 21 different tiles, but the set contains two copies of the 11 tiles of the "sky" suit, so there are 32 tiles in total. pagat.com Traditionally the 1 and 4 spots are red, as are half the spots of the double 6, in Pagat's wording on that page (the page itself writes "Tradionally"). pagat.com Following the convention of Chinese dice, the one pip and the four pip are always coloured red. The other pips are all coloured white, except for the double six. pagat.com The tiles are longer and narrower than the "double square" shape used in the West. They have no dividing bar in the centre to separate the two ends. pagat.com Chinese dominoes are always flat faced and can be stacked. Western games leave the tiles loosely spread on the table in a "boneyard"; Chinese games build a "woodpile" by stacking the tiles. pagat.com
More on Chinese tiles, and how they relate to Western ones, is on the history page.