Server Object Model:
1-SharePoint itself uses the server object model.You can also use this model on a sharepoint server bcz it has some dependencies satisfied by the sharepoint server.
2-Here you can use LINQ programming like LINQ to SharePoint.
3-different classes are there like SPFarm, SPServer, SPService, and SPWebApplication etc.
Client Object Model:
1-Client Side APIs refer to the Client Object Models that were introduced in SharePoint 2010.
2-It is available in three different flavors like: .NET managed,Silverlight and ECMAScript.
3-The Main advantage of the CSOMs is that you do not need to be on the Server to use them in your program. The .NET client object can be used in any Desktop or Web Client. The Silverlight CSOM can be used in silverlight applications and you can call the JS Client Object Model directly from your web pages.
Managed Object Model
Silverlight client object model
Different types of Objects:
Server object model