What's the difference of the oldest light and newest light? Excuse an amateur question, as inspired by this question: "How old is the oldest light visible from Earth?", how to determine the age of light? Does light get old? Does light have characteristic therefore we know this light "A" is different from that light "B" therefore we can track how it going over time? Like tagging animals to observe their activities? How to differentiate one light from the other?
There is no measurable difference between an "old" photon and a "new" one. A photon has a wavelength, a polarisation, and a direction of travel. And no other features. 

You may ask if it is meaningful to discuss the age of light. It is certainly possible to say that photons were emitted by a certain body 100 years ago, and these photons are being detected now, and so this light is 100 years old. But it is impossible to measure the age as a property of the light.

We don't know of any characteristic that uniquely specifies the "age" of the light, so we just assume it's travelled from as far away as we think the object that generated it is, and call the time to travel that far it's "age".  In the case of the Cosmic microwave background, this was (we think) released when the universe first became transparent, a few hundred thousand years after the "big bang". The light from this far back has been "stretched" by the expansion of the universe, but not changed by time.

This is normally true of many simple objects. They either exist or not. A proton doesn't age. A neutron may decay, but this is an event, not a process. It is only with complex objects made of many particles that they can change with age while maintaining their identity.