Judgment is how you judge if [somethingA] is [somethingB]. How do you know if the sky is blue? You can use your eyes to look at the sky, this is one form of judgment. You can use a camera to take a picture of the sky, then use your eyes to look at the picture, that’s another form of judgment. You can trust what I tell you about the color of the sky, that’s another way of judging (more about Judgment). Judgment is used to build up a reality (see What is Reality, Truth, and Existence?): the sky is blue, the grass is green, etc.
Logic is how you update a reality once a judgment is made. Let’s say at 3PM you look at the sky and it is blue, so you live in the reality of “the sky is blue.” Then at sunset, you look at the sky and see that it is red. Seeing that the sky is red is a judgment. It takes logic to translate that judgment into an update of your reality from “the sky is blue” to “the sky is red.”
See this in action in the second example of Properties of Reality