Understanding the adaptor pattern (c#)

I have a scenario I am coding, where I feel the Adaptor Pattern would be useful. I have a service that has multiple possible providers I want to switch when I like, so as long as each "Adapter" follows the same rules (interface) the underlying code is hidden from the caller.

With this in mind, I've been looking at a number of examples. This code snippet is taken from this stack overflow example:

Interface ITarget
{
  public void GetData();
}

//Decision to use MSDAO
class AdaptorMS : ITarget
{
  public void GetData()
  {
    MSDAO objmsdao = new MSDAO();
    objmsdao.GetDataMethod();
  }
}

// calling code
class Client
{
  static void Main(string[] args)
  {
    ITarget objAdaptor = new AdaptorMS();
    object dummyObject = objAdaptor.GetData();
  }
}

Then we decide to create a new adaptor that we will change to:

//After a month, the decision to use OracaleDAO was taken, so create a new adapter
class AdaptorOracle: ITarget
{
  public void GetData()
  {
    OracleDAO objrracledao = new OracleDAO();
    objoracledao.GetSomeData();
  }
}

// Calling code
class Client
{
  static void Main(string[] args)
  {
    ITarget objAdaptor = new AdaptorOracle();
    object dummyObject = objAdaptor.GetData();
  }
}

I've also seen this example:

public class AdaptorA : ITarget
{
     private TargetA A { get; set; }

     public AdaptorA( TargetA a )
     {
           this.A = a;
     }

     public void GetData() { 
          return this.A.SomeGetDataCall(); 
     }
}

public class AdaptorB : ITarget
{
     private TargetB B { get; set; }

     public AdaptorB( TargetB a )
     {
           this.B = a;
     }

     public void GetData() { 
          this.B.MakeDataCall(); 
     }
}

We have two new adaptors but what I don't understand about the above example, is the fact the Adaptor class takes a parameter for the underlying system it will call (TargetA or TargetB). What's the difference in the two examples? I get the first example, hiding all implementation from the calling code (instance of OracleDAO is inside the adaptor), but not the second. Is there a fundamental difference or have I misunderstood the pattern?

Thanks in advance for any advice!