Maybe it's because this is not the same classes.

Look at MSDN :

• Thread.CurrentPrincipal
  • IPrincipal
    • IsInRole
• WindowsPrincipal
  • IsInRole

So, if there are differents classes, maybe there are differents implementations.

EDIT :

I have try this code :

public class InGroup
{
    public string Name { get; set; }
    public bool Current { get; set; }
    public bool Fixe { get; set; }
    public bool Thread { get; set; }
}

WindowsIdentity current = System.Security.Principal.WindowsIdentity.GetCurrent();
WindowsPrincipal principalcurrent = new WindowsPrincipal(current);

WindowsIdentity fixe = new WindowsIdentity("JW2031");
WindowsPrincipal principalFixe = new WindowsPrincipal(fixe);

IPrincipal principalThread = System.Threading.Thread.CurrentPrincipal;

List<InGroup> ingroups = new List<InGroup>();
foreach (IdentityReference item in current.Groups)
{
    IdentityReference reference = item.Translate(typeof(NTAccount));
    Console.WriteLine("{0}	{1}	{2}	{3}",
        reference.Value,
        principalcurrent.IsInRole(reference.Value),
        principalFixe.IsInRole(reference.Value),
        principalThread.IsInRole(reference.Value));

    ingroups.Add(new InGroup()
    {
        Name = reference.Value,
        Current = principalcurrent.IsInRole(reference.Value),
        Fixe = principalFixe.IsInRole(reference.Value),
        Thread = principalThread.IsInRole(reference.Value)
    });
}
foreach (IdentityReference item in fixe.Groups)
{
    IdentityReference reference = item.Translate(typeof(NTAccount));
    if (ingroups.FindIndex(g => g.Name == reference.Value) == -1)
    {
        ingroups.Add(new InGroup()
        {
            Name = reference.Value,
            Current = principalcurrent.IsInRole(reference.Value),
            Fixe = principalFixe.IsInRole(reference.Value),
            Thread = principalThread.IsInRole(reference.Value)
        });
        Console.WriteLine("{0}	{1}	{2}	{3}",
            reference.Value,
            principalcurrent.IsInRole(reference.Value),
            principalFixe.IsInRole(reference.Value),
            principalThread.IsInRole(reference.Value));
    }
}

And here is the result

As you can see, I did not have the same groups with differents ways. So (because I'm administrator of my local machine) I think that WindowsIdentity.GetCurrent will get the user from AD and WindowsPrincipal(WindowsIdentity("")) will get the user from local machine.

In my webapp, I have got the lowest authorisation possible (I think). But, I have no explanations for the consoleapp...

It's only suppositions, but this is coherent.