What is the difference between the two? I mean the methods are all the same. So, for a user, they work identically.
Is that correct??
From the (dated but still very useful) SGI STL summary of deque:
A deque is very much like a vector: like vector, it is a sequence that supports random access to elements, constant time insertion and removal of elements at the end of the sequence, and linear time insertion and removal of elements in the middle.
The main way in which deque differs from vector is that deque also supports constant time insertion and removal of elements at the beginning of the sequence. Additionally, deque does not have any member functions analogous to vector's capacity() and reserve(), and does not provide any of the guarantees on iterator validity that are associated with those member functions.
Here's the summary on list from the same site:
A list is a doubly linked list. That is, it is a Sequence that supports both forward and backward traversal, and (amortized) constant time insertion and removal of elements at the beginning or the end, or in the middle. Lists have the important property that insertion and splicing do not invalidate iterators to list elements, and that even removal invalidates only the iterators that point to the elements that are removed. The ordering of iterators may be changed (that is, list::iterator might have a different predecessor or successor after a list operation than it did before), but the iterators themselves will not be invalidated or made to point to different elements unless that invalidation or mutation is explicit.
In summary the containers may have shared routines but the time guarantees for those routines differ from container to container. This is very important when considering which of these containers to use for a task: taking into account how the container will be most frequently used (e.g., more for searching than for insertion/deletion) goes a long way in directing you to the right container.