Is there a difference between readonly and { get; }

No, the statements do not mean the same thing. The full version of the property will have a backing variable:

private int _x;

public int X
{
    get { return _x; }
}

Another method in the class could modify the backing variable, changing the value of the property:

private void SomeMethod(int someValue)
{
    _x = someValue * 5;
}

The readonly keyword only allows a member variable to be assigned in its declaration or in the constructor:

// Both of these compile

private readonly int _x = 1;

public SomeClass()
{
    _x = 5;
}

// This will not compile

private void SomeMethod(int someValue)
{
    _x = someValue * 5;
}

So a get-only property whose backing variable is marked readonly is a true read-only property.

readonly int x; declares a readonly field on a class. This field can only be assigned in a constructor and it's value can't change for the lifetime of the class.

int x { get; } declares a readonly auto-implemented property and is, in this form, invalid (because you'd have no way whatsoever to set the value). A normal readonly property does not guarantee to return the same value every time it is called. The value can change throughout the lifetime of the class. For example:

public int RandomNumber
{
    get { return new Random().Next(100); }
}

This will return a different number everytime you call it. (Yes, this is a terrible abuse of properties).

In answer to your question: There is a difference between readonly and {get; }:

In int x { get; } (which won't compile as there's no way to set x - I think you needed public int x { get; private set; } ) your code can keep changing x

In readonly int x;, x is initialised either in a constructor or inline and then can never change.