Thanks. What quick responses!

Based on waitecj's first reply, I realised my problem.
I was connected with sys as sysdba to the second instance.

To open up the first database, I had to re-connect with

connect sys/pwd1@db1 as sysdba

I could then open up the first instance/database.
I could even switch back to the second with:

connect sys/pwd2@db2 as sysdba

and open up the second instance/database simultaneously!

It's obvious that I'm quite new to this, but I've learnt a great lesson!

I still don't know the implication of setting the ORACLE_SID environment variable as bazza suggests, since I didn't do that, and it still seemed to work. Likewise I don't yet understand the TNS set up and the significance that has. However.....there's all that still to learn....

Cheers,
Don