I am not sure that I can answer your question completely because different schools might use different terminology, but I can certainly give you some ideas that might help you.
A lesson plan is a highly structure document. It includes the name of the class and the date the lesson is to be given. It has sections for objectives, materials, activities, procedures, differentiation, and extensions. I am going to make a guess that notes for a lesson are an abbreviated form of a lesson plan that you might keep with you in the classroom to help prompt you from one activity to the next. Certainly, few teachers have time to sit down and look at a formal lesson plan as they are teaching, particularly in elementary school.
I am not really sure about the names of all these different boards, but a magazine board would most likely include articles written by the students, while a group display board might include work created by a particular group in the classroom. For example, if there are different groups for reading, each group might have its own display board.
I hope this helps. Good luck to you.