The idea behind this "conceptual breath" stuff is from those that are more in visuddhimagga tradition that clearly separate samatha/vipasasana. So they say in discerning differences in breathing you are recognizing impermanence thus its a vipassana practice, so you want to solidify the breath or as its put bellow "just mentally knowing the presence of the breath". Further for this group the mental nimitta (sign, image) that one can solidify their attention on is important. But there are different views and ideologies. I'm sure if you seach google for "jhana dhammawheel" you will have a lot to read.
"The basic difference between mindfulness of breathing as a samatha or as a vipassana practice depends on what angle is taken when observing the breath, since emphasis on just mentally knowing the presence of the breath is capable of leading to deep levels of concentration, while emphasis on various phenomena related to the process of breathing does not lead to a unitary type of experience but stays in the realm of variety and of sensory experience, and thus is more geared towards the development of insight." - Analyao p.130
My suggestion would be not to place so much emphasis on jhana, something you are not too sure about anyway. Don't put the cart ahead of the horse they say. There are prior things you can place emphasis on such as the factors of jhana, and mental hindrances.
withdrawn from sensuality, withdrawn from unskillful qualities — enters and remains in the first jhana: rapture and pleasure born from withdrawal, accompanied by directed thought and evaluation. He permeates and pervades, suffuses and fills this very body with the rapture and pleasure born from withdrawal.
quite secluded from sensuality, secluded from unskillful qualities — entered & remained in the first jhana: rapture & pleasure born of seclusion, accompanied by directed thought & evaluation. Whatever qualities there are in the first jhana — directed thought, evaluation, rapture, pleasure, singleness of mind, contact, feeling, perception, intention, consciousness, desire, decision, persistence, mindfulness, equanimity, & attention
Monk, having abandoned six things one can enter and abide in the first jhāna. What six? Sensual desire, ill will, sloth & torpor, restlessness & remorse, doubt; and the danger in sensual pleasures has been well seen with right understanding inaccordance with reality.’