to see: to take something in, whether with the eyes or with the mind, so that it registers and is known
This is one of the main verbs for seeing in the New Testament. Its root idea is not just that light hits the eye but that something is actually taken in and registered. So the same word stretches naturally from looking at an object in front of you, to grasping a truth, to the deep claim that someone has genuinely beheld God.
The writings of John lean on this verb again and again, almost always in a form that means "has seen" and still carries the effect into the present. When the disciples say "we have seen the Lord," they mean they were eyewitnesses and that what they saw still stands behind their testimony. The same word then drives John's biggest claims: no one has ever seen God, yet whoever has seen Jesus has seen the Father.
In the future tense ("you will see") the verb often points ahead to a promised sight, including the final hope of seeing God's glory. And in a worn-down command form ("see to it," "watch out"), it becomes a warning to stay alert, the way we still say "see that you don't forget" without meaning anything about the eyes. These are all the same verb doing different jobs, held together by the idea of taking something in so that it truly registers.