D&D 5E Psionics relates to Ki

[OB1]

I tend to think of it in terms of the world being a computer simulation.

Divine Power - Appealing to the Users to write code or activate cheats to help you directly.
Arcane Power - Discovering bits of code written into the simulation that allows you to change the simulation in predictable ways. Can come through study, inherent coding of your avatar, or through appeal to daemons
Ki Power - Intuitive understanding of the fact that you are a computer simulation, giving you the ability to accomplish superhuman feats
Psi Power - Through intensive study, directly hacking the machine code running the simulation to allow you to do otherwise impossible things.

 

[machineelf]

They come from the same source in my game, though do different things.

The source for Arcane power is from mastery of the arcane magical weave around the world.
The source for Divine power comes from the gods and them granting it to you.
And the source for ki and psionic power comes from mastering the power within oneself.

EDIT to add: I also perceive as ki being something one studies rigorously to achieve, whereas psionic is something one is born with, but can enhance with some practice. In other words, it is similar to the difference between a wizard studying the arcane ways vs. a sorcerer begin born with an innate ability.

I may change my conception and relation of ki and psionic once they put something more official out about psionic powers, and may alter the concept based on campaign setting.

 

[DMCF]

A monk goes "Hi-Ya!" With every kick or punch.

A psionic goes "Womph Womph" continually like a heavy rolling bass.