Remeber these from back in the day

My club would give these out when you shot at the required level I had some at 50 yards but can’t find those 

I still have a box full of those with added Bars. My dad was never into guns, but we belonged to the IBM Country Club ($3.50 per year) as he spent 51 years with IBM and many of my Hobbies started there. 
HAM RADIO CLUB
PHOTOGRAPHY CLUB
JUNIOR GOLF TEAM
and Indoor and Outdoor Shooting

Bob

The NRA still has similar awards for the "NRA Marksmanship Qualification Program" for Rifle, Pistol and Shotgun.

Details can be found here:  
NRA Marksman Qualification

The various patches, certificates and badges/pins can be ordered here:
NRA Programs Materials

I don't recall the medals, but do remember seeing the patches. Usually there were several  sewed on a shooting or field jacket. Another patch display was the large Perry patch and the yrs in sequence below. These were down the center of the back with mfg or the award patches alongside. Don't recall seeing the Distinguished patch on 'em. That patch covered all of the above !
Ron Habegger

Up north, they were patches. Here's an example of the old ones from the Shooting Federation of Canada (SFC)

There were NRA provided "State Team" patches passed out at the State Championships too...