x:Name and Name are referencing different namespaces.
x:name is a reference to the x namespace defined by default at the top of the Xaml file.
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
Just saying Name uses the default below namespace.
xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
x:Name is saying use the namespace that has the x alias. x is the default and most people leave it but you can change it to whatever you like
xmlns:foo="http://schemas.microsoft.com/winfx/2006/xaml"
so your reference would be foo:name
Define and Use Namespaces in WPF
EDIT:
OK lets look at this a different way. Say you drag and drop an button onto your Xaml page. You can reference this 2 ways x:name and name. All xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" and
xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml" are is references to multiple namespaces. Since xaml holds the Control namespace(not 100% on that) and presentation holds the FrameworkElement AND the Button class has a inheritance pattern of:
Button : ButtonBase
ButtonBase : ContentControl, ICommandSource
ContentControl : Control, IAddChild
Control : FrameworkElement
FrameworkElement : UIElement, IFrameworkInputElement,
IInputElement, ISupportInitialize, IHaveResources
So as one would expect anything that inherits from FrameworkElement would have access to all its public attributes. so in the case of Button it is getting its Name attribute from FrameworkElement, at the very top of the hierarchy tree. So you can say x:Name or Name and they will both be accessing the getter/setter from the FrameworkElement.
MSDN Reference
WPF defines a CLR attribute that is consumed by XAML processors in order to map multiple CLR namespaces to a single XML namespace. The XmlnsDefinitionAttribute attribute is placed at the assembly level in the source code that produces the assembly. The WPF assembly source code uses this attribute to map the various common namespaces, such as System.Windows and System.Windows.Controls, to the http://schemas.microsoft.com/winfx/2006/xaml/presentation namespace.
So the assembly attributes will look something like:
PresentationFramework.dll - XmlnsDefinitionAttribute:
[assembly: XmlnsDefinition("http://schemas.microsoft.com/winfx/2006/xaml/presentation", "System.Windows")]
[assembly: XmlnsDefinition("http://schemas.microsoft.com/winfx/2006/xaml/presentation", "System.Windows.Data")]
[assembly: XmlnsDefinition("http://schemas.microsoft.com/winfx/2006/xaml/presentation", "System.Windows.Navigation")]
[assembly: XmlnsDefinition("http://schemas.microsoft.com/winfx/2006/xaml/presentation", "System.Windows.Shapes")]
[assembly: XmlnsDefinition("http://schemas.microsoft.com/winfx/2006/xaml/presentation", "System.Windows.Documents")]
[assembly: XmlnsDefinition("http://schemas.microsoft.com/winfx/2006/xaml/presentation", "System.Windows.Controls")]