What is the difference between abstract and concrete data structures?
The abstract data type (ADT) is essentially an API, and a concrete data structure provides an implementation of that API. For a given ADT, there are often several different choices of concrete data structures which support the query and update operations described by the ADT. Every concrete data structure for a given ADT must support all the operations described by the ADT (possibly with some probability of success in the case of randomized structures), but each concrete structure may make different guarantees of the running times of each operation. The choice of which concrete data structure to implement for a given ADT usually depends on the priorities of efficiency of each operation (including initializing the structure) and the complexity of implementing and maintaining the various data types. Some concrete data structures have excellent theoretical guarantees, but the overhead is such that a slightly less theoretically optimal data structure may be a better choice in practice. 

There are far too many ADT and corresponding concrete structures to list in a single answer, but here are a few examples:


A dictionary supports Find(x) queries. For an a key $x$, return the element in the dictionary with key $x$, if such an element exists. A dynamic dictionary also supports Insert(x) and Delete(x). Common implementations of a dictionary include different kinds of balanced binary search trees (e.g. red black tree) and various kinds of hash tables.
In addition to Find an ADT may require support of successor(x) queries. That is, maintain a set of keys $S$, and given key $x$, find the smallest key $t \in S$ such that $s &lt; t$. Concrete data structures which support the Successor ADT include various binary search trees, and more complicated structures such as an X-fast trie or van Emde Boas tree (if the keys are integers).
A Priority Queue is an ADT that requires insert and delete-min operations (and sometimes other operations as well, such as find-min increase-key or delete-key). Data structures that implement the priority queue ADT include: 


an unsorted linked list, which has fast insert but slow delete-min.
a sorted linked list which has fast delete-min but slow insert
a binary search tree, which has logarithmic insert and delete-min, and $sort(n)$ initialization time.
a binary heap which has logarithmic insert and delete-min, and linear time initialization.
There are also other variants of heap implementations.

An interval stabbing ADT maintains a set of intervals on the real line, and supports a stabbing(x) query, which returns the subset of intervals which contain (are stabbed by) the point $x$. Data structures that implement the stabbing query ADT include a Segment Tree and an Interval Tree.