Can I change the Continue Shopping button by store? I want one store to link to an ETERNAL site whereas all others can link back to site home page.
Do you mean the button-link at the checkout-success-page?
The url is not changable by backend configuration.
Either you have to extend the template
by including this condition:
<?php if (Mage::app()->getStore()->getCode() == 'your-store-code'): ?> ... <?php endif; ?>
or set a new template for the success-block in the layout xml file
... <STORE_[store_code]> <reference name="checkout.success"> <action method="setTemplate"> <template>[.*].phtml</template> </action> </reference> </STORE_[store_code]> ...
Decide on your needs.