Will the same license key work for a Sitefinity 3.x and Sitefinity 4.x website on the same domain?
No, the Sitefinity 4.x license keys are different than the 3.x license keys. If you have an existing Sitefinity 3.7 website, after upgrading your project to 4.x you need to download the 4.x license key from your Sitefinity client account and apply it to your project. The 4.x license key will be for the same domain name as the 3.7 key. Both 3.x and 4.x license keys will remain available for this domain name.