Real photo postcard
In 1903 Kodak introduced the No. 3A Folding Pocket Kodak. The camera, designed for postcard-size film, allowed the general public to take photographs and have them printed on postcard backs. They are usually the same size as standard vintage postcards (3-1/2" x 5-1/2"). Also known by the acronym "RPPC".
Kodak's 3A camera pioneered in its use of postcard-size film but was not the only one to make Real Photo postcards. Many other cameras were used, some of which used old-fashioned glass plates that required cropping the image to fit the postcard format.
According to this site, Kodak "created a service called “Real Photo postcards,” enabling people to make a postcard from any picture they took" in 1907.
While Kodak was certainly the major promoter of photo postcard production, they didn't seem to originate the term "Real Photo," and used it less frequently than photographers and others in the marketplace from 1903 to ca. 1930. But it has become the popular term nowadays to distinguish photographic postcards from commercially printed, mass-produced postcards of the same era.
Old House Journal states "Beginning in 1902 Kodak offered a preprinted card back that allowed postcards to be made directly from negatives."  Regardless of when the year, this technology allowed photographers to travel from town to town and document life in the places they visited. Old House Journal continues: "Local entrepreneurs hired them to record area events and the homes of prominent citizens. These postcards documented important buildings and sites, as well as parades, fires, and floods. Realtors used them to sell new housing by writing descriptions and prices on the back. Real Photo postcards became expressions of pride in home and community, and were also sold as souvenirs in local drug stores and stationery shops." 
March 1st, 1907 was a pivotal day in the history of Real Photo postcards. On that day, Federal legislation allowed, for the first time, that users could write a message on a "penny postcard". Prior to that time, the address only was allowed on one side while the other side could present a photo or artwork. After 1907, the backs of postcards were divided, allowing the address on the right side, while a message could be written on the left side of the blank. The reverse side could then accommodate a full-size real photograph. Popularity of Real Photo postcards soared nationwide. There became a postcard craze in America, and many people began collecting the cards in albums. No other single format has provided such a massive photo history of America, particularly of small-town and rural America where photography was often a luxury.
Real photo postcards have made for millions of one-off photographs, where the photographer may have produced a single or a small number of prints from one negative.
Real Photo postcards may or may not have a white border, or a divided back, or other features of postcards, depending on the paper the photographer used. Many current Real Photo postcards are reproductions of earlier historic photos. Want to know if it is authentic or a reproduction: look at it under a magnifying glass. If it is authentic "it will show smooth transitions from one tone to another."  According to the 2Buds, the way to tell is, while looking under the magnifying glass notice that "Postcards that are NOT Real Photos are made up of many small dots. If you look at a Real Photo postcard, the image is solid (no dots)." 
Bernhard, Willi: Bernhard Picture Postcard Catalogue: Germany 1870-1945, 1982
Bogdan, Robert and Todd Weseloh: Real Photo Postcard Guide: The People’s Photography. Syracuse, NY: Syracuse University Press, 2006. ISBN 0-8156-0851-9, 288 pages, 367 black-and-white photographs, appendixes, bibliography, notes, index.
Morgan, Hal & Brown, Andreas: Prairie Fires and Paper Moons: The American Photographic Postcard: 1900-1920, David R. Godine Publisher, Boston, 1981 (1st), ill., 192pp
Nicholson, Susan Brown: The Encyclopedia of Antique Postcards, Wallace-Homestead Book Co., Radnor, PA, (1994) 1st ptg, 1100+ postcards ill in B&W, 277pp, fine, wraps (softcover), Covers more than 100 categories of postcards from the Golden Age (1898-1918), including artists from Attwell to Wayne and topics from Aviation to the Zodiac. Each category includes a brief history and examples of typical postcards. Includes a price guide.
Sante, Luc: Folk Photography: The American Real-Photo Postcard 1905-1930, YETI Books, 2009, ill., 159pp.
Smith, Jack H.: Postcard Companion: The Collector's Reference, Wallace-Homestead, Radnor, PA, (1989), B&W and color ill., 374pp. Good source book on all aspects of postcard collecting.
"Dating Post-1920 Real Photo Postcards," by Ernest G. Covington, in Postcard Collector, July 1986, pages 26-28.
Harvey Tulcensky and Laetitia Wolff: Real Photo Postcards (Princeton Architectural Press, 2005)
Vaule, Rosamond B.: "As We Were: American Photographic Postcards, 1905-1930," David R. Godine, Publisher, Boston, 2004. 216 pages, 230 duotone photographs, bibliography. Exceptional paper, print, photo reproduction quality. Text addresses social, commercial, and photographic history; real photo makers, subjects, production, and use.