Again, looking at this from the viewpoint of abhidhamma may help put an end to a pursuit in which words can never catch.
First, a comment on:
“I just died and attain full nibbana, obviously being dead, I ain’t going to jump over puddles or anything funny right?, I’m dead AND in full Nibbana so why am I called an Arahant and the Buddha is called a Buddha?”
Parinibbana IS parinibbana; done, fini, finito! There is not a trace of mind and matter left as you said (no rupa, citta, cetasika). There is no you (as you knew it) to jump over anything, and there is nothing to be jumped over.
I would never associate “being dead” with parinibbana. Parinibbana is, if anything, “deathlessness”; being unborn, there is no dying. I bring up this point because many non buddhists have told me something like this: “The goal of your religion is death.” Birth and death apply to the world of 31 realms (rupa, citta, cetasika).
To your question of the difference between a buddha and an arahant, my speculation, using abhidhamma, is as follows:
The case of Parinibbana should be clear by now: no difference between a buddha and an arahant (as you knew them via their rupa, citta, cetasika).
I also mentioned nirodha samapatti, which is like parinibbana in the sense that there are no citta running, but the body is still alive, and therefore there is “coming back” to the world of citta and cetasika.
I would say there is no difference between a buddha and an arahant here. Let’s say two bhikkhus are sitting side by side, and they are both in nirodha samapatti at that time. One is a buddha and one is an arahant, but there is no difference between them.
What about when a buddha and an arahant is going about their day to day lives like the rest of us? Living in the world, they have citta (with cetasika) running as we do, but:
First, we know that the 10 fetters (samyojana) are no more in them.
We also know that no asobhana (non beautiful) cetasika arise in their citta. Only sobhana (beautiful) cetasika arise in their citta.
Here there could be a difference in the citta of a buddha and that of an arahant. sobhana cetasika may arise in different combinations in the citta of a buddha as in an arahant. There may also be different degrees of “beautifulness” of the sobhana cetasika for a buddha and for an arahant.
Again, sheer speculation — about buddha and arahant — from someone who is not even a sotapanna. But hopefully it satisfies curiosity of this nature.