Excerpted from this link:
https://www.vgl.ucdavis.edu/services/dog/GeneticDiversityInToyPoodles.php
"The Poodle has been bred in several sizes and Standard, Miniature, and Toy Poodles are recognized by the American Kennel Club. The British Kennel Club also recognizes three sizes. The Fédération Cynologique Internationale (FCI) recognizes the three sizes variants but adds in the medium Poodle.
The different sizes are not considered breeds, but rather varieties with the miniature and toy being merely smaller versions of the standard. Crosses between various sizes are allowed and offspring registered based on height at the withers. However, the trend is to select parents within the same size range more like breeds. ***This was a surprise. Not sure which registry is being referred to here.***
The Standard Poodle sets the size for the three (or four) different varieties of Poodles. Most kennel clubs state that an adult Standard Poodle must be over 15 inches (38 cm) at the shoulder, while the FCI sets the size for standards at 18-24 inches (45-60 cm). The adult Miniature Poodle must be 11-15 inches (28-38 cm) at the shoulder in registries other than the FCI, where the size range is 11-14 inches (28-35 cm). The slightly smaller size range for Miniature Poodles and higher size range for Standard Poodles in the FCI is to allow for the Medium (Moyen) variety at 14-18 inches (35-45 cm). Toy Poodles are from 7-10 inches (17.8-25.4 cm) in height and 6-9 lbs (3-4 kg) in weight.
There is a theory that Maltese or Havanese may have been crossed to poodles prior to the 1800’s to produce Toy Poodles as suggested by the silky coats found in early toys.1 The present DNA-based study also boosts this theory. The first Toy Poodles depicted in Europe were usually white or white with markings and used to hunt truffles or act as companions. Small white toys from the European continent are thought to have been the foundation for the breed in both the UK and the US. Toy Poodles (which were white) were established as a breed in the United States as far back as 1896 and the first Toy champion was recorded in 1910. Shortly after that time Toy Poodles were accepted as a breed by the AKC, separate from other Poodles. These early Toys were small (3.5 to 5 lbs.) and did not have the same type as the Miniature and Standard Poodles. The breed standard proposed by the International Toy Poodle Club in Philadelphia was published by the AKC in the official book of breed standards in 1929 and had a required weight maximum of 12 pounds. A height maximum of 10 inches was added subsequently to prevent larger dogs from dominating in shows1.
According to Mackey Irick (“The New Poodle”, 1986),1 many US Toy Poodles can be traced back to CH Happy Chappy, born in 1932 bred by Florence Orsie. Happy Chappy is also the sire of the first colored Toy champion, a silver produced by breeding him to a silver miniature. In 1940, registration papers were revoked for these inter-variety offspring with the argument that these dogs were not true Toy Poodles. Research presented by EE. Ferguson to the AKC resulted in a reversal of this decision, and Toy Poodles were placed within the Poodle breed as a size variety instead of as a separate breed in 1943.
Between the 1940s and the 1980s many Toy to Miniature crosses were done to try to improve the type of the existing Toy Poodles and add new colors. This type of breeding continued until the 1970’s or 1980’s, after which most breeding was kept mainly within the variety and within colors1. Although the result of crossing the original Toys to Miniatures improved head, length of leg, length of body, and coat, it has made it difficult to produce well typed dogs within the desired height of 9.5 to 10 inches at the shoulder. The height issue continues to be one of the biggest challenges for breeders2. The Toy Poodle continues to have several different colors that succeed in the show ring and strict within color breeding is no longer the norm.3 Combinations of red/black, brown/black, black/white, silver/white are more commonly found together in pedigrees than others.
1Mackey J. Irick, Jr. “The New Poodle 6th Edition”, Chapter Howell Book House, New York, NY 1986
2Christi McDonald, “Toy Poodles: 40 years ago and Today”, Poodle Variety April-June 2016, p 114
3Christi McDonald, “Beyond Black and White”, Poodle Variety July-September 2016 p 12.
Mufar42, just substitute "variety" for breed

. (But in another of the UCDavis genetic history of Miniatures there is a reference to Miniatures being a genetically different breed from Standards. Just gets more confusing, doesn't it!)
The bold print is mine. I wonder if this is why some toys go oversize?
My boys are an oversize toy/small mini cross and ended up at about 14" and 13" at the shoulder. We call them mini's.