I was just there over this weekend, they sold us those 9 eur train tickets saying you can use it for any train anywhere. Then we board the first train that Apple Maps suggested and the first thing we hear from the announcer "9 eur tickets are not valid on this train".
The 9 euro ticket is only for local and regional trains. However, you can just get about anywhere taking only local and regional trains, but it'll be a very long day.
I'm pretty sure any train from BER airport would be covered under the 9-euro ticket. The trains not covered under the ticket are primarily ICE (inter-city high speed) and anything operated by another company (e.g. FlixTrain).
Yes from BER, it was an IC, but we didn't actually need to go to another city, it just happened to stop near where we were going in Berlin and be the fastest way to get there (first option that navigation apps suggested).
Ended up fine, just got on some slower train that was fine for those tickets.
It was a nice option to have, because normally it seems we would've paid like 50 euros or something to get around for three days. But it was weird that the tickets reset on the 1st of the month, so we had to buy two of them because of unlucky timing.