Silverlight Runtime is a plug-in for browsers to support Silverlight enabled applications. If Silverlight runtime is not installed, browsers will not be able to run Silverlight elements in the browser. You can set up your Silverlight tags such a way that your browser will automatically prompt the user to download and install the Silverlight plug in when your application is launched in the browser.
Installing the run time is a one time operation on the client. Once installed, it will be automatically launched when any Silverlight application is loaded in the browser.
Silverlight SDK is a set of tools, documentation, samples and templates for the web developers to help them easily develop Silverlight enabled applications. The SDK is not really mandatory to develop Silverlight applications, however, SDK will make development much easier.