I know you have not actually done an upgrade, but effectively you have.
The 2.3 database will not run in 2.4, there have been many changes, most noticeably in your case references have changed to reflines, so you need to continue with your upgrade:-
Its all explained in the update.html file which is in FA's root directory - Please read this 1st - I've completed many upgrades by following these instructions and never had a problem.
There are 2 parts to the upgrade, the software upgrade and the database upgrade, from your description and the screenshot, it 'looks' like you have done the software upgrade, now you need to do the database upgrade - I think you need to go to Setup - Software Upgrade (this is really the database upgrade), this should show you that you have an upgrade - click the 2.4 upgrade and it will make the necessary changes in the database. It will take a while to make the necessary changes, this will depend on the size of your database.
To answer your question
In which folder exactly there is a update script for the document Change or reference 'UPDATE' .
Its in the "sql" folder. Have a look at the sql in this file and you will see that it corresponds with your screenshot errors. You could run this directly in myphpadmin, but the software upgrade works fine and I've used it numerous times.