Hi Howard:
I belong to ASM (Materials Information Society), so I went there and looked up their definitions of the two terms. Here is what is in the ASM Metals Handbook Glossary of Metalurgical and Metalworking Terms;
Coating
A relatively thin layer (<1 mm, or 0.04 in.) of material applied by surfacing for the purpose of corrosion prevention, resistance to high-temperature scaling, wear resistance, lubrication, or other purposes.
Plating
Forming an adherent layer of metal on an object; often used as a shop term for electroplating. See also electrodeposition and electroless plating .
If you'd like to do a little more research for whatever the reason you are asking, I would recommend going to their Website,
http://www.asminternation.org and snooping around. Hope this helps - or at least points you in the right direction...
-Steve