Looking connotes activity while seeing is simply passive.
"Therefore speak I to them in parables: because they seeing see not" (Matthew 13:13, emphasis mine) Parables. Stories, allegories, fanciful tales. Life altering words strung together by one who is not only a master storyteller, but also the arbiter of human existence? All of the above. It's all in the eye of the beholder. "Therefore when thine eye is single, thy whole body is full of light." (Luke 11:34)
The commands of Jesus straddle the strata of human experience. When He says "as ye would that men should do to you, do ye also to them likewise" (Luke 6:31), it applies to everything we do and every type of person we encounter. At whatever station in life we find ourselves. Whatever hat we wear, whatever mask we don, we cannot escape this simplest of commands. Each level of life brings with it its attendant issues and difficulties. And if we're not "looking unto Jesus" as it says in Hebrews (12:2), then our focus will be off, our eyes will glaze over and we'll be blind. The antidote to simply seeing is actively looking.
"Looking for that blessed hope, and the glorious appearing of the great God and our Savior Jesus Christ." (Titus 2:13)
Jesus is the north star. True north. And I'm not talking about some outmoded and artificial symbolism. He is the one whom we live and move towards whether we realize it or not. In this He's also like the sun (a star) and if we find ourselves squinting from brilliance, we're looking in the right direction.
"Who being the brightness of His (God the Father's) glory, and the express image of His person, and upholding all things by the word of His power, when He had by Himself purged our sins, sat down on the right hand of the Majesty on high." (Hebrews 1:3) This being said, if we're not actively looking to Him, bringing all our faculties to bear to realize Him, then the only direction left to look is inward. This might sound untrue, but think about it. Humans need a point of contact from which to actualize. Be it ultimate self-actualization or simply the realization of a dream directed outward. Even if you strive to be the most selfless person in existence, eschewing cynicism in the face of the greater good, however nebulous that goal may be, you must have an anchor from which to launch out. And any endeavor without God in view is selfish. "I'm doing this because I want to." Fair enough. But you're not looking in the right place. Consequently, you're seeing God all around you yet doing nothing about it, because your vision is directed inward. Christians! I'm not just talking to the atheist and non-believer.
"Jesus answered them and said, Verily, verily, I say unto you, Ye seek me, not because ye saw the miracles but because ye did eat of the loaves, and were filled." (John 6:26)
How do you look? Do you see through the symbolism to actuality? God speaks in ways that are multi-layered. On one level, all religions and myths are allegorical. Meaning that you can take or leave the historicity of the stories and add to your life the kernels of overarching truth. Seen this way, Jesus (whether or not He ever truly existed) is a good teacher. If you're having trouble with the moral law, take what He says on forgiveness and "lov[ing] thy neighbor" (Matthew 22:39) and go about your business. Existential crises? The mythic aspect of who He was might appeal to you. Frame an artist's rendition above your headboard and look to it wistfully before you retire. But what is it that drives the point home that Jesus came to "save sinners; of whom I am chief." (1 Timothy 1:15), and actually meet Him on those grounds? The conviction of the Holy Spirit will cause the scales to fall from our eyes and we'll see Jesus as all that and more. Humility.
"Then shall the King say unto them on His right hand, Come, ye blessed of my Father, inherit the kingdom prepared for you from the foundation of the world: For I was an hungred, and ye gave me meat: I was thirsty, and ye gave me drink: I was a stranger, and ye took me in: Naked, and ye clothed me: I was sick, and ye visited me: I was in prison, and ye came unto me. Then shall the righteous answer Him, saying, Lord, when saw we Thee an hungred, and fed Thee? or thirsty, and gave Thee drink? When saw we Thee a stranger, and took Thee in? or naked, and clothed Thee? Or when saw we Thee sick, or in prison, and came unto Thee?" Look: "And the King shall answer and say unto them, Verily I say unto you, Inasmuch as ye have done it unto one of the least of these my brethren, ye have done it unto me." (Matthew 25:34-40)
"A king that sitteth in the throne of judgment scattereth away all evil with His eyes." (Proverbs 20:8) He'll do it for us.