It would be a whole different database. The two instances would not share any resources, they would be completely distinct entities.

On a production box, you would have one group of processes and memory structures named "PROD". The "PROD" database would have it's own lgwr, dbwr, smon, pmon, ckpt, etc processes. The "TEST" database would also have its own set of lgwr, dbwr, smon, pmon, ckpt, etc. processes. The two databases would be totally independent of each other.