setappdata sets the value of the 'ApplicationData' field of the figure, while set can set the value of all fields of any kind of handle graphic objects. In your example set is used to define the 'String' property of the object with the handle stored in handles.response. But the struct handles (which has a confusing name, because it can contain everything and not only handles) is stored by guidata(), which is a wrapper for setappdata and getappdata for convenience.
Even setappdata(Handle, Name, Value) is a wrapper for:
S = get(Handle, 'ApplicationData');
S.(Name) = Value;
set(Handle, 'ApplicationData', S);
Using setappdata(0, ...) stores values in the application data of the root object, which means the command window. This is a kind of global variable with the usual difficulties.