It is essential to use at least working definitions while speaking of the several distinctions that you are making. It is also necessary to cite to support a statement, such as. “Cognition is a process of being conscious from a state of unconscious.” If we define cognition in terms of consciousness, how do we define consciousness, and in terms of what? And your reply implies that recollection/remembering is not cognitive. Then what?
Another implication from what you say is that most of the time, we are not cognizing. Most of our experiences are repeated again and again. We see the same things that are familiar to us year after year, day after day, minute after minute. If this awareness, which is close to 100% of our experiences, is not part of cognition, then cognition is a narrow window. This may not be a problem as long as the major part of it has some name to it, and all of that is part of some broader term. To be best of my understanding most academic practice recognizes that to be cognition, within which we sub-classify other modes of cognition, including conscious and unconscious. And not the other way round as you state.
Cognition as a process of being conscious from the state of unconscious, means consciousness is part of cognition. There is an overlap between the two. However, we also need to distinguish between cognition and consciousness.
In very simple terms ‘Cognition is a mental process of knowing’. All the processes such as thinking, remembering, reasoning, problem-solving, decision making, memorizing and recollecting back from subconscious what was already in our cognizance are part of cognition as they help in knowing. However, knowing simply doesn’t mean being aware about it.
Therefore, ‘conscious cognition equates to awareness’, Conscious cognition is to be aware what it is and what it means. While unconsious cognition is to know without being aware, it can include procedural memory, a habitual memory.
Cognition can be hence be concious or unconcious. The difference being, when the term consciousness is used, its more than a Cognitivist computational view of the mind as a machine. Machine doesnt have consciousness similar to human beings. Consciousness is an emergent property of interaction of human being with external world, and more closer to Cognitive psychology.
Congnition is almost involved in everything we do and all mental process that go about it, however all cognition cannot be called conscious in nature.
Some try to distinguish between the two by bringing in subjectiveness such as intents, motives and needs-driven actions of individuals to demarcate conscious cognitive actions from unconsious cognitive actions.