LinkedList: Is stored in memory as a contiguous array
No its not. The elements are represented by an internal Entry class (very much like Map.Entry). Arrays are not involved.
ArrayList: Is stored in memory as blocks.
The internal data structure is an array, if that is what you meant.
Traversing through all the elements will always take O(N) time. Be it an ArrayList or a LinkedList.
Obtaining any particular element at a given index is another question. With an array backed ArrayList, it is as simple as returning array[index]. With the LinkedList, one has to traverse through the members using Entry.next until the element at the given index is reached. The worst case is O(N) for LinkedList, while for ArrayList the retrieval operation is always O(1).
As for insertion, LinkedList can grow its structure without copying over elements, while arrays do not have this luxury.