How do the 4 jhana and 4 arupa jhana they relate?

You could say that the 4 arupa jhanas are a “modification on the topic” of the fourth jhana or a “variation on the same theme”.

They bear its characteristics but push it with regards to its topic. Have a look at Leigh’s very nice description of this “transformation on the fourth jhana”

5. Sense the “boundaries of your being” and begin pushing them outwards:

a. Push outwards until you fill the room,

b. Push outwards until you fill the building,

c. Push outwards until you fill the neighborhood,

d. Push outwards further and further, remain focused on pushing outwards,

e. When an infinite space opens up before you, switch your focus to it.

6. Realizing that it takes an infinite consciousness to be aware of an infinite space, switch your attention to to your consciousness of the infinite space.

7. Switch your attention from the infinite consciousness to the content of that consciousness – it will be an infinite emptiness – no-thing at all anywhere.

8. Let go of all the previous outward sensing and come to rest in a small spot more or less between the eyes and a few inches from your face.

Focus should thus be first on mastering the 4
That (their playing with concepts, no added value, as we may say) may well explain why the Buddha gave up on the 4 arupas jhanas, but came back to use the 4 jhana as a foundation for his enlightenment. Oh, this looks like another topic for a posting:
Anapanasati-4jhana-vipassana-3vijjas…puh!