The Microsoft.RuleEngine assembly can be used by any .NET application. The BizTalk Server can be considered as one of the consumers of BRE. The Microsoft.BizTalk.RuleEngineExtensions is the extension for BizTalk to provide some additional functionality. The main difference is that the Microsoft.BizTalk.RuleEngineExtensions.RuleSetDeploymentDriver writes out information to the BizTalk tracking database so that rules can be tracked using HAT. If you use the Microsoft.RuleEngine.RuleSetDeploymentDriver class, deployment go a little bit faster (no need to save the rules to the tracking database, but it is not recommended.
In general, you should use the one configured. In BizTalk 2006, the static method Configuration.GetDeploymentDriver() determines what has been configured and returns an instance of that class. This method looks at the registry entries DeploymentDriverAssembly and DeploymentDriverClass under HKLM\Software\Microsoft\BusinessRules\3.0. The default values for these keys are Microsoft.BizTalk.RuleEngineExtensions and RuleSetDeploymentDriver. In other words, the recommended way is to use the one in Microsoft.BizTalk.RuleEngineExtensions namespace.