Integer is a simple field that allows you to store and show integer values. Unlike the Number field you cannot store decimal values here. For an integer field you can also set up a prefix and suffix that will be visible during content editing.
A Selection field is used to show a predefined list of items available to select during editing. This way you can be sure that you will not make a typo during edition. Also you can be sure that the value used in this field will be taken from a predefined list - no wrong values anymore!
Group field is a kind of “virtual” field that cannot be displayed on a template, but is visible in the editing view. Thanks to the Group field you can better organize your fields schema, and optimize your editing.