The answer is no. Your service ports and connection ports should not be the same and usually you will set the connection ports to 0-0 to allow the operating system to assign ports as required. Your service ports will depend on what processes are running which communicate with other processes in your backup zone - you need to open 7937 and 7938 plus two further ports (7937-7940 is easiest). If you have a storage node process running you need an additional two ports per tape drive and a port for each library and the server process will require an additional 7 ports (remember the client process runs on the storage node and the client and storage node processes run on the server). Ports opened should allow TCP/UDP traffic both ways.
If you wish to run the NMC from that client there are some ports you need to configure there too.

In the past figuring this out has been a bit of a black art but these days there is a big section in the admin guide that explains it all clearly - probably worth taking a look at so you understand it all a lot better.

Please review the Appendix in the Admin Guide it is explained thoroughly. Just as a quick note the port setting on your client is not correct for the Connection ports. Connection ports should be set to 0-0 for versions after 7.4.x and 10001-30000 for older versions.

Regards...

Yes, but if it's set to 0 - 0 on the client, could it not negotiate something that the FW prevents?

I will have a look in the Admin Guide, maybe this will give me some answers

No these are source ports and are negotiated in the TCP handshake. Stateful packet inspection on the firewall keeps track of the source ports and allows return communication on those ports. So, it is okay to have at 0-0 and it does not mean to "Open no ports". What it means is "Let OS decide what ports to use".

Regards...