In order to customize the Final Confirmation Page only for the subscription confirmation you would need to create your own custom ConfirmSubscription.aspx page. You can find the page in the EXM folder \sitecore modules\Web\EXM\.
If you take a look at the default implementation in the file Sitecore.EmailCampaign.Cd.dll (Sitecore.EmailCampaign.Cd....
It is pretty straight-forward in Sitecore Forms. You can achieve this using Submit action.
Open Sitecore Forms, in your form, drag-and-drop a submit button from the Form Elements pane (Structure section), if it is not already present.
select the Submit button
On the Form Elements pane, expand the Submit Actions section, click the Add button
Click on ...