Is there a difference between the red sky in the morning and in the evening? It certainly has a different feeling to it, but
does the temperature or earth's rotation or the clouds
or anything else really make it two different physical
phenomena or at least different colors?
Or is it pretty much the same spare the direction? 
 A: Here is an excerpt from [https://www.loc.gov/rr/scitech/mysteries/weather-sailor.html]:

Red sky at night, sailors delight.
  When we see a red sky at night, this means that the setting sun is sending its light through a high concentration of dust particles. This usually indicates high pressure and stable air coming in from the west. Basically good weather will follow.

Red sky in morning, sailor’s [take] warning.
A red sunrise can mean that a high pressure system (good weather) has already passed, thus indicating that a storm system (low pressure) may be moving to the east. A morning sky that is a deep, fiery red can indicate that there is high water content in the atmosphere. So, rain could be on its way.
The color of a sunrise or sunset is caused by the same "stuff" in the atmosphere, but the meaning is different, as any experienced sailor will attest to.  One reason that sunrises and sunsets look and feel different is because at the time of a sunset, we've spent the last 8 hours or so in relatively bright conditions, so our eyes are adapted to the brighter light.  In the early morning, our eyes are adapted to darker conditions.
A: 
It certainly has a different feeling to it, but does the temperature or earth's rotation or the clouds or anything else really make it two different physical phenomena or at least different colors? Or is it pretty much the same spare the direction

The 'red' color is due to the fact that the light is scattered greatly - the rays travel a larger distance through the atmosphere (because the sun is near the horizon) unlike in noon when the sky is more blue (because the sun is overhead and does not travel at any significant angle). 
Tiny particles in the atmosphere can scatter light - air molecules or particulates. If you look through what Rayleigh scattering is (the scattering is proportional to the inverse fourth power of the wavelength of light) you will get a better sense of what it is. Blue light is scattered easily, and the red comes at the end of the line. 
Now, at sunrise and sunset, the sun is near the horizon and is going to move out of our sight (so the light rays have to travel further). 
A: Ideally, there should be no difference, but of course there is a difference, and you can note it anytime: evenings are more reddish, and it is not due to the Doppler effect (altough it is everywhere, but it can be negligible).
The thing is that, in the evening, there are many more particles in the atmosphere, and consequently there's much more scattering, so you see the sky mroe red. The main contributions are:


*

*Pollution, accumulated all along the day.

*The main cause: humidity. At night, it's much colder. Cold air admits much less proportion of water than warm air. Read about saturated-vapour pressure.


During the night, as it is cold, the air doesn't carry much water. When that air gets warm, it becomes dryer. Even if it keeps the same mass of water, the relative humidity is lower, because being warm it could admit much more.
So, in the mornings, there's much less humidity and less pollution. Therefore less scattering. That's why dawn is less reddish than dusk.
