The class of admission pertains to the visa category under which you were admitted. For example, someone who got the green card through a spouse would have a different class of admission than a child, or a parent etc. If you have a copy of your green card, your class of admission would be stated on it.
This would usually be on your resident card.
This would be the manner of admission, did you enter as a child of a USC or a husband or another class of admission.