In simple English language :
identification is the activity and analytical process of being able to recognize an unknown object and name it.
classification is the statistical analysis leading to being able to place an unknown object into a category (defined by known and quantified parameters) of objects.
For example, based on the presence of (a) 2 legs, (b) 2 arms & hands, each bearing 5 fingers each (c) one head with 2 eyes, 2 ears, one nose, one mouth, 2 lips, etc etc, you may be able to 'classify' an unknown animal into the species Homo sepiens. But being able to put a tag of Ramesh / Naresh / Harish/ ... will require many more attributes to be recognised for the unknown animal. Once you have them, you will be able to 'identify''!
The same principle applies to pattern recognition.
Being able to identify an unknown object, say as the 'Rashtrapati Bhavan' requires you to know of its location, geometry, etc, etc, etc.... But, to be able to classify it as an 'building' requires much lesser information. Whether you get that information from image data. ground truthing, 3rd party sources, or a-priori data is not relevant, so long as you have the information.
It's quite simple really identification is the process of picking out an individual do to specific circumstances or characteristics, very similarly classification does to put you into a group based off characteristics but this is a group or category instead of an individual identity this is the biggest difference between the two the number of things being classified or identify.