Installing and upgrading help

Bob,

Yes, you should use a different database for each instance, each with its own db user.

(Otherwise they will be the same instance and write all over each other in the same database which will create chaos. Now, while in theory you could use the same db but a distinct table prefix, but I would never do this in real life in a production instance. It is much better - safer, more secure, easier to manage, better performing  - to use two distinct databases.)

While technically you can use the same db user and password for each database, I would never do this in production. I would make them distinct, each database having its own sql user each with privileges to just its own database. 

So:

production config.php

$CFG->dbtype    = 'mysqli';
$CFG->dblibrary = 'native';
$CFG->dbhost    = 'localhost';
$CFG->dbname    = 'productiondb';
$CFG->dbuser    = 'productiondbuser';
$CFG->dbpass    = 'somepassword';
$CFG->prefix    = 'mdl_';

sandbox config.php

$CFG->dbtype    = 'mysqli';
$CFG->dblibrary = 'native';
$CFG->dbhost    = 'localhost';
$CFG->dbname    = 'sandboxdb';
$CFG->dbuser    = 'sandboxdbuser';
$CFG->dbpass    = 'anotherpassword';
$CFG->prefix    = 'mdl_';

Note it is okay that the table prefix is the same in each database, since they are separate databases.

You will of course need to manually create the Sandbox database, its user, and grant it the proper privileges, before starting the install.