There is a difference.
And this is due to scattering, namely the blue component of the spectrum being scattered the closer the sun is to the horizon. So in sunsets, the sky gets redder and redder, whereas at sunrise the sky gets, relatively, bluer and bluer.
So then the colour balance is different for sunrise and sunset. For sunrise, the highlight will be close to daylight colour balance, whereas for sunset, it will be towards shady. Colour balance for shadows are cold for both, eg fluorescent, and the midtones somewhere in between.
Use the colour balance tool in Photoshop to tweak the colour balance in each of these zones, using the eye as the judge.
And also as you may have guessed by now, no out-of-cam sunrise/sunset will be accurate, as the camera uses only a sngle colour balance point for the whole scene, when in reality it is a complex mix of colour balances.