How have you hooked up the event? the way you've described things, it's only the button that you've hooked up to the OnClick, in which sender will always be TButton, and never TRadioButton.
For each RadioButton, ensure it's onclick is pointing to your buttonclick handler.
Other than that, your posted snippet looks good and should work, Can you post a more complete example?
Alternatively: In the ButtonClick simply reference each component by name, that way you won't need .Tag at all.
It's kind of hard giving a generic answer without knowing exactly what you're trying to achieve.. So, what are you trying to acheive? :-)