Patanjali in his Yoga Sutras discusses these three concepts in relation to intensive concentration or samadhi. This word samadhi is much misunderstood and we will come back to that.
Grahya is the word given for objective, grahana the instrument, and grahita the subject. Our language reflects these basic concepts. For example we have a sentence : I see a dog. Dog is the object. The dog could be my dog, hairy dog, dog on a roof, dog on my roof, dog who is ill... There are many qualifications that can occur through the objective layer. In fact we even confuse the subject and object. For example: I am a good person or I am a bad person. I am this, I am that. In sentences such as these we qualify the subject with the object and end up confusing the two. This is one of the major problems that Patanjali discusses in his sutras, a problem called avidya or ignorance of our real nature.
The objective realm is the realm of thought, of mind, of qualification, judgement, analysis. Many branches of knowledge, including those of liberation such as the yoga end up functioning through this realm. It is a realm of discontinuity as it separates and divides and individualizes an infinite array of form/name concepts.
When we come back to the sentence "I see the dog", the seeing itself is the instrumental layer. This seeing by itself can also become confused by the object as this objective layer tends to dominate the seeing. If I am in a room full of dogs and "I see many dogs", the concept of dog is going to fill our consciousness. The seeing itself is overlooked. When we come truly into the seeing we realize that it is pure in and of itself. Vasistha confirms this in his Yoga Vasistha when he says the senses by themselves are pure, it is the mind that pollutes them.
Many traditions not realizing the confusion of the instrumental and objective layers, see the problems inherent in the objective layer and tend to "throw the baby out with the bath water", attempting to dismiss the sensory layer in an effort to overthrow the objective element. This misses something big.
All of the senses when dived into fully reveal something vast, something continuous. It is here that we find the meaning of nebulous terms such as energy or prana. These concepts can only be discovered within this realm. However it is a bit tricky. The objective layer is like a vast horizontal continuum, seemingly going on forever. To truly find the instrumental layer, we cannot go horizontally like we have been doing. We have to dive. We have to go down. In. We have to shift to the vertical axis. This takes us into a realm that underlies the constructs of mind and the objective layer.
We find in this instrumental layer a vast continuity. It is not discontinuous. This continuity leads us right back to the subject. The experiencer of all experiences. And this is very different than the qualified I. It is pure in itself. It is clarity, luminosity, brilliance, awareness, presence. Our words do not fully do it justice.
The process of mudra which leads to samadhi takes us into this realm. Vyasa in his commentary on Yoga Sutra 1.1 tells us that samadhi is present in all states of mind. This gives us a clue that intensive concentration and ultimately samadhi are not something that is created. It is not something that is built by discontinuous elements of the objective realm like we might think. This mode is problematic and involves a very difficult task. It is rather something that is discovered. Or rather uncovered. It is an uncovering or discovering of the continuous nature of ourselves. Once this is tasted one has to habituate to it and recall how to "remember". This is smrti. Not mindfulness but rememberance. Not remembering like we remember a thought but remembering on the deepest level. Kind of like an attuning to something. Then it is just a slight reorientation of will at the deepest level that causes the unmesa/revealing of the luminous/continuous and the nimesa/disappearance/resolving of the discontinuous.
If we orient in this way we will have success. Patanjali tells us that we first need shraddha or faith, then energy, then smrti. Only then will we discover/uncover the nature of the continuous and arrive at samadhi. Holding to this through continuous habituation, we come to prajna or wisdom of our fundamental nature.
This is the process of mudra.