Hi,
Thanks for using our plugins. I can help out here.
We did not change any of the field names from 3.5 to 3.9
There has been template modifications and function changes.
If you have any custom templates in your theme or custom coding, I would look to update those.
As for the update you can use the automatic update system to update or deactivate and delete 3.5 and then upload 3.9 to your site and you should be all set.
It is always a good practice to backup the site beforehand just in case something happens.
Let me know if you have any follow up questions.
Thanks