There are many ways to achieve this, but I would recommend it by overriding the template file.
To do so, just copy the file
/vendor/magento/module-catalog/view/frontend/templates/product/list.phtml and put it under
Now you can programmatically check whether a customer is logged into the website or not, and based on that you can change the value of __('Add to Cart') to whatever you want.
Since the solution needs some custom code, it is not possible by simply writing the translation in the translation files.
The above solution is the simplest one and it also does not break any Magento standard.