What is the difference between HttpContext.Current.Request.IsAuthenticated and HttpContext.Current.User.Identity.IsAuthenticated?

There’s absolutely no difference. Checkout HttpContext.Current.Request.IsAuthenticated implementation:

public bool IsAuthenticated
{
    get
    {
        return (((this._context.User != null) && 
                 (this._context.User.Identity != null)) &&
                 this._context.User.Identity.IsAuthenticated);
    }
}