SSS
Both? Throw the International Single Shot Assoc. (ISSA) into the mix and you have three organizations.
The bigger question is why are there three schuetzen organizations. 
That question has been debated for over a decade.

Are the targets the same with all groups?

Can sorta understand the A & I thing. Not that many of us speak a language other than English, and we are rather USA rifle-centric. However, as am relatively new here, am not aware of the history/difference between the ASSRA and WY Sch. Other than, perhaps, I understand that the WY Sch is pretty strict about being BP only and we seem to be fine with smokeless loads.

SSS
The WSU, ASSRA and ISSA all use the same German 25-ring target. Each organization prints it’s own version but the scoring rings are the same size for all three.
To sort out the differences and similarities you need to go to the organization’s web sites and read their rules. It won’t take long for you to figure out that the three groups have more in common than they have differences. Be aware that the similarities and differences are very real though.
One good thing is that you should be able to shoot the same rifle and equipment in all three groups in both open and traditional classes. 
Joe threw in the NRC which is affiliated at least loosely with the WSU and is a bench rest only group. WSU being offhand only.
Hope this helps

At that match the shooters got together and formed the ISSA to continue the Coors type matches. They started to print their own targets and looked for a home for their match. The NRA Range at Ratone was a new facility then and the matches were moved to Ratone the next year. It has been shot there every year since. 
  Over the years the two organisations have developed separately along a generally similar path. The ISSA Has, over the years had a number of changes to their targets, some compatible with the ASSRA and some not. To this day you will find many shooters who shoot both clubs events and some local clubs who have a bewildering mix of both.   
The WSU is the newest kid on the block. It was formed by Steve Garbe in response to what Steve thought was an unacceptable relaxation of tradition. Their focus is geared more toward black (or original) powder original or original reproduction rifles. 
  While we have more in common than divides us there are still very real differences between the organisations. Many shooters belong to all three and shoot by the rules that govern at what ever match they happen to be at. 
In the end we are all single shot shooters and it is my hope that at some point we can get individual egos out of the equation and hammer the three Associations back together. Kind of like a Damascus barrel.

40 Rod

A couple of minor clarifications:
40_rod
You missed the first Coors match date by a couple of decades but you did end the year with a "?" The first Coors match was in 1982, last was in '92. ISSA formed in 1993 after the Prairie Dog match in SD.

mes
ISSA scoring rings extend to target edge. Hits outside the printed scoring rings are scored using an overlay (in other words - a shot hitting outside the 14 ring would be scored with the overlay and might be a 13, 12, 11 . . . out to the target edge)

Other than those two points, I think you guys pretty much nailed it.

Crash
Of course your right it was 82, this is what I get for writing off the cuff before I have had all my coffee. 
The extra scoring rings are what I was talking about when I said that there were small but significant differences. The extra scoring rings on both targets give the opportunity for higher scores thus although they are the same size bull and rind with they are ineligible for records in the ASSRA. 
Slowshooter, you are right that is the way the old matches were shot. When you went to the line and the hammer fell you were scored on where the bullet went, no hole no score. It is a rule that I agree with. The problem comes down to the way we shoot now from individual benches there is no way to verify that the rule is followed. Add in either money or nice prizes and the cheating skyrockets. The temptation, for some, becomes too great and a few otherwise honest shooters cross the line. Some egos just can't bear to not be in the top three. In the words of Reagan "trust but verify. 

40 Rod

40 Rod

This is my take on why there is a separation of powers in the single shot game........... Like 40 Rod said, single shots were a small group until the Coors matches came along (I've posted in the past that Coors did more for this sport than any other single thing).

Now, had the ASSRA stepped up and held a truly national match to replace the Coors Schuetzenfest, today there would be only one single shot organization. One that had nation wide respect and with the money that could do many things to promote this dying area of interest. And like the Coors matches, would have the national shooting sport magazines clamoring to cover it.

At this point, I really don't think that there is anyway to rectify the problem. The leadership of the ASSRA has only focused on the Etna Green area and that's all it has ever done. I don't know if that is to keep from loosing control of ASSRA or if it is just because they can not see that the betterment of the sport is to cater to everyone from shore to shore (by cater, I mean help all affiliated clubs put on,promote and advertise matches). It also builds respect by letting everyone know they are really apart of the organization.

I know that some will be upset by what I'm saying but, it is the truth and it is sad that after all these years that we haven't progressed past the "Coors days" at those days will become known as the zenith of the single shots in modern times. 

People that have studied the sport know that it used to hold the popularity of than the NFL has today and that the prizes awarded were where worth at least $50,000 of today's dollars and that you could make a good living shooting the bigger matches. 

That is what I would like to see!!!

Frank