I'm wondering whether when people refer to concentration meditation such as shamatha, they mean that there is still conceptual thought or its absence.
For example, I am capable of meditating upon an object, e.g. breath, and focus with an intensity that no thoughts or very few emerge. However, I am also capable of simply paying attention to the object while thoughts emerge, but I redirect attention to the object when thoughts have done so.
I am basically asking whether genuine concentration is more like the first or the second. What exactly is referred to by absence of thought, or the fact thought helps meditation until the jhanas. Do we mean gross thought, such as sentences and ideas, or do we mean the intelligence of awareness, discernment?
If possible, can anyone relate this with calm abiding and special insight, and what is meant by these terms?