The "bronze stars" are campaign stars, designated to be worn on a medal ribbon (in this case, the European-African-Middle Eastern Campaign Medal) for each designated campaign (a combined geographic area and time period, defined by the War Department) participated in by a unit, and by extension the individuals assigned to that unit. Campaign stars are different than the Bronze Star Medal, awarded for meritorious service or valor in combat.

The 357th Fighter Squadron was awarded credit for participating in the "Normandy," "Northern France," "Rhineland," "Ardennes-Alsace," and "Central Europe" campaigns and also was awarded credit for the "Air Offensive, Europe" campaign, for participation in air combat operations in the area of the European Theater prior to 6 June 1944. War Department General Orders No. 33 and No. 40, 1945, defined the geographic areas and time periods of campaigns; General Order No. 40 updated the conditions of General Order No. 33. Battle participation credit for individual units was awarded in separate general orders.

Your grandfather's military occupational specialty, presumably at discharge, was 941 (camera technician); this is a ground position distinct from 940 (aerial photographer):

CAMERA TECHNICIAN (941)

Adjusts, maintains, and repairs all aerial and ground, still, and motion picture cameras used by Army Air Forces. Makes periodic inspections of cameras and laboratory equipment, and repairs defects using precision hand tools. Selects equipment to be used on photographic missions, and checks for proper functioning of such mechanisms as film timing and automatic and semiautomatic features of cameras. Prepares reports on installation of cameras in airplanes. May repair gun cameras.

On 1 December 1943, each single-engine fighter squadron (Table of Organization and Equipment 1-27) was composed of an "air echelon" of thirty-five officers and eighty-six enlisted men (pilots, aircraft ground crews, and "immediate" maintenance personnel) which included two camera technicians (one staff sergeant and one corporal) in the technical section, and a "ground echelon" of four officers and 159 enlisted men (additional maintenance personnel devoted to more complicated tasks, and personnel to support routine squadron operations) which included two camera technicians (one sergeant and one corporal) in the technical section.

Information on the discharge paper:

• 1.) Name

• 2.) Army Serial Number. Since the number begins with a 3, your grandfather was drafted or volunteered for induction. The second number is also a 3, meaning he entered military service in an installation of the 3rd Service Command (Maryland, Pennsylvania, Virginia, or Washington, D.C.)

• 3.) Grade held at discharge

• 4.) Branch of the Army; Army Air Forces

• 5.) Component of the Army; Army of the United States.

• 6.) Organization. This could be either the last organization a man was assigned to before discharge, or the organization with which he spent the most time in service.

• 7., 8.) Place and date of separation from military service.

• 9.-21.) Personal identifying information collected before entry into service. In classifying civilian occupations, the Army used the numerical codes in the Dictionary of Occupational Titles.

• 22.-29.) Information concerning circumstances of entry into military service. Your grandfather was inducted on 20 July 1942, and then was placed in the Enlisted Reserve Corps on furlough (varying from seven to twenty-one days, depending upon the time period) until 3 August 1942, during which he would have had time to conclude his affairs if he had not already done so, before reporting to a designated reception center to have his military records initiated and receive further orders.

• 30.-34.) Information concerning military service. Box 30 is often the last military occupational specialty a man was assigned, rather than the only one he had held during his service. Additional information regarding assigned military occupational specialties and duration can be found in the Separation Qualification Record (WD AGO Form 100). As noted above, your grandfather was awarded the European-African-Middle Eastern Campaign Medal with six campaign stars. The 357th Fighter Group received three Distinguished Unit Citations (for Berlin, Germany, 6 March 1944, Leipzig, Germany, 29 June 1944, and Derben, Germany, 14 January 1945). He also received the Good Conduct Medal for one year of infraction-free service in wartime. He also would have been entitled to the World War II Victory Medal, although being created in July 1945, it often does not appear on discharge papers until late 1945. Boxes 32 and 33 are often "incomplete," either for want of space in the boxes, or lack of immediately available information at the separation center.

• 35.-42.) Additional information concerning military service and civilian experience.

• 43.-57.) Pay and insurance information, and remarks. The "lapel button" is the Honorable Service Lapel Button, issued to be affixed to retained Army-issued shirts or jackets to denote a veteran had been honorably discharged and to allow him to legally wear his uniform for a time post-discharge. The "ASR score" is the Adjusted Service Rating score, a sort of "seniority" system developed in fall 1944 to determine eventual priority for discharge. This box also often contains information on time (or lack of time) lost under Article of War 107, under which men absent without leave were required to make up time lost, and state National Guard service prior to date of induction into federal service for men who served in the National Guard in the 1940-1941 timeframe

Sources:

United States. Department of the Army. Unit Citation and Campaign Participation Credit Roster. Washington, D.C.: Department of the Army, 1961.

United States. War Department. War Department Technical Manual 12-427 Military Occupational Classification of Enlisted Personnel. Washington, D.C.: United States Government Printing Office, 1944.

Just to add to the other answers:

As u/the_howling_cow kind of suggests, it is entirely possible your grandfather received training in aerial photography in larger aircraft even though his ultimate assignment in the combat theater appears to have been as camera technician in a fighter squadron, which was a ground position. So if there are stories about grandpa taking pictures from a nose of a bomber, they are probably true--but they should probably be understood as stories about training flights. Flying, even in training was always exciting and dangerous, and over 15,000 American aircrew perished in training accidents.

Confusing the bronze star device for the Bronze Star Medal is very common. It's just confusing terminology! To add to the confusion, keep in mind you would not actually pin a large number of bronze star devices to a ribbon: they would not fit. Instead, every five bronze star devices would be replaced by a single silver star device.

So if you want to recreate your grandfather's medals, you should attach one silver and one bronze star device to the EAME Campaign Medal ribbon.

See https://www.archives.gov/veterans/military-service-records to request records and copies of medals. Note many records were lost in a fire, details here: https://www.va.gov/records/get-military-service-records/reconstruct-records/ You can request WWII Victory Medal that is not indicated on the discharge papers based on his service. Also, check for alumni associations that often have unit histories if you want more info.