Onesie or onesize is American English for a bodysuit for infants; it is designed to conceal a diaper when worn. It is also known as a One-Piece, Baby Grow , creeper, diaper shirt or snapsuit. The British equivalent is referred to as babygro. Onesie is a genericized trademark registered to Gerber Children swear, Inc. Babygro is also a trademark brand, and was invented in the U.S. in the 1950s by Walter Artzt.
The shirt extends past the waist and has snaps or buttons that allow it to be closed at the base, offering support to a diaper. Onesies are often worn by infants in place of shirts due to their ability to stay tucked, which is difficult to maintain with infants wearing regular style shirts. They are worn commonly by very small children. Onesies TM make wonderful gifts for expecting or new mothers. They are sometimes incorporated into party games played during a baby shower. One popular game is for guests to custom decorate plain Onesies TM prior to the arrival of the expecting or new mother.
(Ref: dictionary.com)

One of the more popular brands of infant bodysuits is Onesies (pronounced /'w?nzis/; "ONE-zees"), manufactured by Gerber Childrenswear (formerly part of Gerber Products Company). The terms "Onesie" or "Onesies" are sometimes used in the United States as if they were a genericized trademark;[1][2] however, "Onesies" is a registered trademark of Gerber Childrenswear, which objects to both the usage of the term as a generic name and the usage of the singular form "Onesie".
(Ref: en.wikipedia.org/wiki/Onesie)

It should be noted we feel the baby clothing industry views the word, "onesie" TM as a style of clothing, not a particular brand. We are unable use the word "onesie" unless the item is a Gerber onesie TM. The Laughing Giraffe ® refers to its Non –Gerber Onesie as either an infant bodysuit, snap suit, one-piece, creeper, romper or body gro.