In pattern recognition we use detection when we have two sets of classes. Actually it's a binary choice and the final answer is Yes(means belong to target category) or No. We use Classification when we have more than two classes and we want to assign every input to its class.
As others have said, face detection is an attempt to detect faces in an image (or video, I guess). Face detection software will typically provide the location and face size/orientation of each region of the image it feels is probably a face. In my experience, the results can be quite noisy. Depending on how the detection parameters are set, you may get many non-faces and will likely miss some/many faces (especially if they are partially obscured).
Face recognition, on the other hand, attempts to identify a face in an image that is known (or thought to) contain a single face. Face detection may be applied first to extract image segments containing faces. A database of face data for individuals is needed, and the face recognition software will attempt to associate the provided image with one or more records in the database, typically with a probability that the faces match.
Many have given the answers: Face detection aims at the detection/location of face in an image while Face recognition aims at identifying the face with some known faces.
The best example for face detection is our Digital Cameras, you see a square over the faces, when taking photos. Face recognition is usually used in forensics to identify fugitives from street cameras... or something like that.
There are several notions that should be distinguished. Classification = partition of a set of observable objects into disjoint similarity classes (maybe, constituting a hierarchical structure). Detection = in a large set of objects finding out all those belonging to a certain similarity class. Recognition = for a given object answering, to what of (a priori defined) similarity classes it belongs. Identification = a particular case of recognition: proving that a given object really belongs to a similarity class being declared.