The most obvious differences between French Ring and Schutzhund are FR has no tracking, the decoy (helper) wears a full body suit, the dog can bite anywhere on the suit, the order of exercises is random, and when the team walks on the field they complete the entire routine all at once. Sch has the tracking, the decoy only wears a sleeve, and the trial is broken up into 3 portions, tracking, obedience, and protection. With each portion performed with a break between them.
The work of the dog is not as regimented in Ring as it is in Sch. The Ring dog can heel on the left or right, come/recall is any position near handler (front, side, between legs, sit, down, etc.), for the retrieve they just have to be within reaching distance in a sit. The emphasis is more on getting the job done correctly and less on how the job is done. This gives French Ring a more casual feel to it than Schutzhund, where the performance of the dog and handler are being measured against a "picture" of what the perfect performance will look like. There is still strict rules about exercises in French Ring though. If you are supposed to say Fido-out-guard, and you just say Fido-out, it is points off. During the heeling if the dog isn't paying attention and you give an extra heel command, 0 points for the exercise. If you are standing in the wrong spot for a jump, the judge waits until your allotted time for placement runs out, and you get 0 with no chance to attempt a jump. If you walk through the landing zone of a jump you haven't performed yet, 0. If you told the judge you recall with a whistle, and forget and recall with voice, points off. When heeling, if any portion of the end of the leash is sticking out of your hand, or lying on the dogs back, 0. Schutzhund is more concerned with the dogs performing the exercise in a pretty specific pre-defined way. Every dog has to recall the same way (to the front). Speed and enthusiasm is judged. Precision is judged. It's not just about doing the job, it's about how the job is done. Some extra commands are allowed for points off, but not a 0 (within reason). This "get the job done" vs "how they get the job done" attitude carries over into the protection also. In Ring an escort is any position close enough to the decoy to prevent an escape, same with the guard. In Sch the dog is expected to transport in a specific position and manner, and also to guard in a specific way. In Ring the blind search consists of "find and bark" and then the dog does whatever it was trained to do to find the guy. Some circle the field, some run up the middle air scenting, some just randomly run around, etc. In Sch the dog is expected to search the blinds in a specific pattern, as directed by the handler. If the dog misses a blind, whether the helper was in it or not, they will loose points. If they don't look in each blind, but just run past because they think they know where the helper is, they loose points.
In a Ring competition, the dog walks on the field with no leash or collar, and except for the heel on leash does not wear a leash or collar the entire time. If the leash gets tight in the heel on leash, it's an automatic 0. No physical corrections, and limited verbal corrections are allowed. (I.e. you could say "bad dog", but you can't start yelling at the dog). Also, no food is allowed. A Sch dog wears a collar at all times, how much time they spend on vs off leash depends on the level they are trialing at. Although no big corrections are allowed, I've seen dogs with tight leashes, dogs receiving minor leash corrections, etc in the heeling who still earned passing scores. Praise is also allowed in Sch, but not to be overdone (similar to Ring).
When a Ring dog comes out to compete, he/she does all three parts (obedience, agility, and bitework) then leaves the field. A Brevet can take 15 - 20 minutes, a Ring III will take 40 minutes to an hour. A Schutzhund obedience or protection routine takes 8-10 minutes.
Due to the nature of the decoy work, Ring does not judge the dogs grip. As long as they can get the grip and hang on, they will get full points. Sch does judge the grip and assigns a point value to a grip that is full, hard and calm. Sch also wants to see the dogs working in various drives (the serious/defensive barking in the blind vs the prey in a long bite), in Ring as long as the dog is getting the job done, no emphasis is put on what drive the dog is in.
There is a lot more stick work during the bitework in Ring, and the stick is a baton of split bamboo, or rattan tied together to make it flair and clatter. 10 or 15 hits during an attack is fairly normal, and some decoy work includes a lot more than that, I've counted up to 60 in some videos. The stick hits in Sch are delivered at a specific time and manner, with the same number of hits (2) each time.
The Ring decoy has way more leeway in how they work the dogs in Ring, as long as they do not work the dogs above the level they are competing at. Some decoys use mainly agility, some use threatening manners, etc. Each dog is to be initially approached and worked in the same manner as all the other dogs at that level. But if the decoy sees a weakness in the dog, they are expected to exploit that weakness to their benefit, and work the dog in a manner which will exploit it as long as they are not causing physical harm to the dog. Their job is to find weaknesses, and steal points from the dog. The Sch decoy is supposed to work every dog in the exact same manner. They all bring their own individual style in terms of how they present a threat, their speed, etc but they aren't supposed to alter their style of work based on issues they see in a specific dog.
Except for the Brevet, the order of the obedience and bite exercises in Ring is drawn at random right before the dog in white comes out. The only set order is agility, obedience, bitework. The order and height of the jumps is up to the handler. The dog in white is a "practice dog". It gives all competitors a chance to see the order of the exercises, the work of the decoy, etc. It also allows the judge to work with the decoys for that level, and "fine tune" what they do and don't want to see done. In Sch the exercises are in a specific order every time. The dog has to jump the same height every time, the handler has no control over that.
In Ring he field layout is decided by the judge. They will decide where the long sit/down is done, the guard of object, the direction for the send away, the direction of each attack, what blind to hide the decoy in, etc. Now that there are no pits for the jumps, they can also decide where they want the jumps to be. In Sch the judge also decides where things will happen, but since the order of exercises is the same each time there is less variables for the judge to work with, and the layout of a Sch field is pretty similar from trial to trial.
For a more visual experience in the differences between the sports check out the following videos: