Data has a Positronic network that makes up his brain. What makes it so special is the speed - it works like a human brain in that it can process both simple and complicated information at greater than human like speeds. How it actually works though, I don’t know - all I can really gather is that positrons are clusters of information that relays data from all parts of his body (such as his hearing, sight and movement) in large amounts, so that more data is transferred. I guess you could think of it as a super packet on a super T3 line or something.
As far as the reference in Xenogears, I assume you’re talking about Emeralda, in which case I don’t think so because if memory serves Emeralda is a nanite machine. Nanites, being tiny machines, and positrons (if I’m right), are not tiny machines, then no - it is not a reference.
Cyborg implies a dual nature of human and machine (more like the borg). Data was an android, with a positronic processor.
I don’t know if the Phositronic part was a typo and supposed to be Positronic, but either way, the photon part doesn’t apply. A photon is the mass representation of light. Photons are not nearly so substantial as the term mass might imply, but they are the model used to explain the wavelike properties of light.
For the scientifically interested: Positrons are, for lack of a better definition (that isnt too geeky), VERY tiny, positively charged particals, with a mass that is comparable to an electron. So positronic is sci-fi code-word for superdy-duper electronic, implying that somehow, positive particals being transferred along a circuit have a spiffier/faster/more effiecient effect than a system of inverted sub-atomic polarity.
Short version
Data = Android, and not cyborg
Photon = measurable(ish) unit of light, in terms of matter
Positiron = Electron with identity crisis