I managed to find a rail map here, https://sl.se/en/in-english/getting-around/sl-service-network-maps/ .
This does not include buses and ferries though. It only includes all transport on rails. Including buses would render the map unreadable. There are a few hundred bus lines in addition to this.
As said before there are no zones in the SL traffic. You will be able to travel on your commuter card in a radius of about 40-50km from Stockholm City.
In case you want to go to Uppsala, you will have to pay for an additional UL ticket for the amount of zones you want to travel. I was not able to find any good info on this, at least not in English, so I recommend asking in the counter if you plan going there.
If you want to go to Arlanda, the railway and station is owned by a private company and you will have to by an additional ticket if you want to go on or off there.