What do we mean by motivation when we are talking about dog training? Let's keep it simple and put it in human terms, 'what makes us want to do, or not do something'. For me, as a dog trainer, it’s one of the most important things to discover about any dog.
There is such a difference in how a dog will respond during a training session depending on what reinforcer (motivation) we choose to use.
I don't believe there is a set reinforcer that should be used for each situation/training session. However, I will consider the amount of arousal (excitement) the dog will have when we use that reinforcer in an any given environment and the training or behavioural issue I am working on. So, for example. I'm probably not going to use a game of tug if the dog is reactive to other dogs or people, that would be adding too much excitement to an already highly aroused dog. I might choose to use a different game in that scenario like scent work (find it), where the arousal level is more balanced.
When using food/toy as a reinforcer people sometimes get stuck where the dog will only work (perform a behaviour when cued) if food/toy is visible. This is a common dog training problem and has its roots at the beginning of the training sequence, we need to teach the dog that the food/toy (reinforcer) is a consequence of the behaviour and to not just follow the food/toy and you will get it. So how do we go about that? We need to train our dogs in such a way that their motivating reward, the food or toys or whatever we are using as a reinforcer will appear after the behaviour.
Let's look at a simple SIT training scenario:
If we are using food to train a SIT, we can lure the dog into a sit position by moving food over the dogs head until the dogs bum touches the ground, as soon as that happens we mark (good) and release the food. This is fine for getting the behaviour started. As soon as your pup can do this about three times in a row, it's important to remove the food from your hand, your dog should follow your hand movement without the food in it and as soon as their bum touches the ground you mark (good) and reward them from the other hand or a treat bag, this will teach your dog to follow your hand signal and they will be reinforced for doing the “sit “ and to not just follow the food.
I think it's always a good idea to find out a few different reinforcers that your dog has so you will have options on what motivator to use in different circumstances.
The bottom line is finding out what makes your dog tick, plan for your training, implement it and have fun together.