These categories and many of the examples given come from 
Terry Barrett. Criticizing Photographs: An Introduction to Undertanding Images 1990, Mayfield Publishing Company, Mountain View, CA For more information and better explanations you can see the book in our library or purchase a copy through Amazon.com

Explanatory Photographs (Barrett's term)
Photos that help us understand something that is hard to see without using a camera.
Examples include the scientific work of Eadweard Muybridge and Harold Edgerton. 
Photos by Bill Owen and Mary Ellen Mark help use understand society and people. 

Explanatory examples
Muybridge animations
http://www.ediblebrain.com/muybridge.htm
Muybridge work and history
http://www.kingston.ac.uk/Muybridge/

Explanatory 
HAROLD EDGERTON 1903-1990 
http://www.wirtzgallery.com/exhibitions/2001/exhibitions_2001_11/exhibitions_he.html
Explanatory  Bill Owens
http://www.billowens.com/.htm
Explanatory   Mary Ellen Mark
Indian Street Performers. India 1981 cat no 207X-001-001
http://www.maryellenmark.com/frames/gallery.html

Interpretive Photographs (Barrett's term)
Made, not taken
Directed and/or Manipulated
examples:
Jerry Uelsmann, Duane Michals, Anne Brigman, Gertrude Kasebier

Jerry Uelsmann Chairs 2001Interpretive 
http://www.uelsmann.net/indexframe.html

Anne Brigman
1869-1950
The Water-Nixie 
1914 / ca. 1940, reworked from earlier negative gelatin silver glass interpositive 
http://www.geh.org/ar/strip81/htmlsrc/brigmanetal_sum00002.html

Gertrude Kasebier, (1852-1934)
Image has been identified as Agnes Rand Lee, and the "heritage" bitterly referred to is the sudden death of her daughter Peggy. [Anastasia Wilkes, Art in America, November 1992] 
http://www.geh.org/taschen/htmlsrc6/m197100420033_ful.html#topofimage

Ethically Evaluative Photographs (Barrett's term)
Ethically Evaluative 
Photos that praise or condemn
Try to produce improvements in society
Examples: 
Dorothea Lange and Walker Evans (Farm Security Administration work), 
Jacob Riis (labor & housing conditions), 
W. Eugene and Aileen Smith (Minamata), Carrie Mae Weems and Gordon Parks (racial injustice)
W. Eugene Smith  Toimoko in Her Bath Minimata, Japan 1972     22" x 16" http://www.rit.edu/~arton/photographs/smith_toimoko.html

Jacob Riis Home of an Italian Ragpicker 1888

Carrie Mae Weems (racial injustice)
http://www.gregkucera.com/weems.htm
See No Evil, 1997 Color photograph 20 x 24 inches Edition/15 

Susan Sontag “Looking at War: photography’s view of devastation and death.” The New Yorker. December 9, 2002.  pp. 82-98.
See this source in Library or purchase at newstands.

Aesthetically Evaluative Photographs (Barrett's term)
“. . beautiful things photographed in beautiful ways. . . nude . . . landscape . . . still life.” Barrett, pg. 64
examples: 
Robert Maplethorpe, Irving Penn, Edward Weston, Imogene Cunningham, Ansel Adams, Minor White, Henri Cartier-Bresson , Gary Winogrand

Theoretical Photographs --Barrett, page 68 (1st edition)
Photography about photography
examples: 
Cindy Sherman film stills, Joel-Peter Witken work about historical art, Sherrie Levine copies of Walker Evans & Edward Weston, Les Krims book Making Chicken Soup.

Cindy Sherman, Untitled Film Still #13. 1978. Collection The Museum of Modern Art, New York.
http://www.moma.org/exhibitions/sherman/index.html

Cindy Sherman, Untitled Film Still #3. 1977. Collection The Museum of Modern Art, New York. http://www.moma.org/exhibitions/sherman/index.html
Theoretical Photography about photography

Sherrie Levine copies of Walker Evans 

Joel-Peter Witken -  Cover photo for Love and Redemption
Photography about photography Theoretical 
http://www.zonezero.com/exposiciones/fotografos/witkin2/