I am not aware of an explanation in the original Pali scriptures of exactly why the terms 'rupa (form) jhana' & 'arupa (formless) jhana' are used.
However, I would guess the term 'rupa' jhana is related to the activity of the nervous system of the entire physical body ('rupa'). For example, just before entering into the 1st (rupa) jhana, the mental stress stored within the physical is completely calmed & the entire bodily nervous system starts to radiate with bliss. Although the physical body & breathing can no longer be felt in the 1st jhana (due to the strength of the rapture-bliss in the brain dominating conscious awareness), the bliss of the entire bodily nervous system is the basis of the bliss of the rupa jhanas. The Pali scriptures state:
He enters & remains in the first jhana...in the second jhana...There is nothing of his entire body unpervaded by rapture & pleasure...MN 119.
As rapture (piti) & then pleasure (sukha) subside, the mind becomes purified & completely clear in the 4th (rupa) jhana; without the sense objects (sensations) of rapture & pleasure capturing consciousness awareness. The scriptures state, in attaining the 4th jhana, whatever physical-breathing activity remains is totally calmed:
Having attained the fourth absorption, inhalation and exhalation have ceased. SN 36.11
To gain a picture of what it means for the breathing to be completely calmed/ceased, MN 43 describes it is the same as a dead body (thus a medical doctor would think the body is dead due to no movement of the breathing despite the life-force of the body remaining alive).
Therefore, the formless meditations (arupa jhana) are described as solely meditations upon consciousness & mentality, without any breathing & feeling sensations from the bodily nervous system being felt.
The features of the formless meditations are described in MN 111, as follows:
Sariputta entered & remained in the dimension of infinitude of space...the dimension of infinitude of consciousness...the dimension of nothingness. Whatever qualities there are...singleness of mind, contact, (mental) feeling,
perception, intention, consciousness, zeal, decision, persistence,
mindfulness, equanimity & attention — he ferreted them out one after
In the 'dimension of neither perception nor non-perception' (4th formless meditation/8th jhana), the scriptures describe the mental sense objects listed above start to disappear/fade & in the 'cessation of feeling & perception' ('9th jhana') all mentality, including consciousness, completely disappears.
Consciousness disappears in the '9th jhana' because there is no more perception & feeling thus, as taught in the scriptures (MN 38; SN 22.53), consciousness cannot arise without any sense objects.
Note: The '9th jhana' (cessation of feeling & perception) is not Nibbana/Nirvana.
In summary, in Buddhism, there are six avenues of sense consciousness. In the formless meditations (as described in MN 111), mind sense consciousness remains (although eye, ear, nose, tongue & body sense consciousness do not operate).