Here's their descriptions in the "Songs of the 5 Steps"
http://www.northaustintaichi.com/Songs% ... 0Steps.htmI may have a book with the original chinese somewhere, but this is the best you get online right now.
Song of Gaze-Left (Douglas Wile Translation)
To the left, to the right, yin and yang
change according to the situation.
We evade to the left and strike from the right
with strong sure steps.
The hands and feet work together and
likewise the knees, elbows and waist
Our opponent cannot fathom our movements
and has no defense against us.
Song of Look-Right
Feigning to the left, we attack to the right
with perfect steps.
Striking left and attacking right,
we follow the opportunities.
We avoid the frontal and advance from the side,
seizing changing conditions.
Left and right, full and empty,
our technique must be faultless.
So the interesting points to me are that the gaze and look are reversed, but then when you get into the text, they both have elements of left and right, as in Chen Zhonghua's take.
Largely the songs are the same general reminders of important points, but the parts of these two that are the most different, the thesis of each, are distinct.
Gaze Left is a counter, when the enemy attack, we evade to the left and attack to the right (knowing the directions themselves are reversible)
Look Right is a feint, we lure the enemy into attacking, move to a highly advantageous position, and attack.
The layer of translation makes it hard to really see how the subsequent lines relate to and reinforce that, I believe a lot of nuance gets lost along the way.
So along with advance and retreat, considering the constructive and destructive cycles of the elements, it's a shorthand for the base combat strategy of taijiquan.
Honestly, you can take it as deep as you like with this, down to the dim mak, if you wish.