readonly means that the field can only be set in the constructor (or in a field initializer). Properties specified in the object initializer are set after the constructor has returned. That is,

TestStruct ts = new TestStruct {
    TestField = "something"
};

is basically equivalent to

TestStruct ts = new TestStruct();
ts.TestField = "something";

(In practice, the compiler may use a temporary variable, but you get the idea.)

readonly means that the field can only be set in the constructor (or in a field initializer). Properties specified in the object initializer are set after the constructor has returned. That is,

TestStruct ts = new TestStruct {
    TestField = "something"
};

is basically equivalent to

TestStruct ts = new TestStruct();
ts.TestField = "something";

(In a Debug build, the compiler may use a temporary variable, but you get the idea.)