Habib,

You say 2 separate lists of products. Does that mean 2 store fronts? It sounds like you only want to share the customer file.

If that's what you want, here is something you can try, without using the MultiSite Module.

Create 2 zen installs in 2 folders like www.mysite.com/store1 and www.mysite.com/store2

Create the tables for each site in the same database. Use a different prefix for each (like store1 & store2).

Edit store2/includes/database_files.php. Find the 2 lines
HTML Code:
define('TABLE_CUSTOMERS', DB_PREFIX . 'customers');
define('TABLE_CUSTOMERS_INFO', DB_PREFIX . 'customers_info');
and change to
HTML Code:
define('TABLE_CUSTOMERS',  'store1_customers');
define('TABLE_CUSTOMERS_INFO', 'store1_customers_info');
Both sites will then use the same customer info and can log into either with the same ID. Everything else will be like 2 stores.

It is important to keep a note of this change as this file cannot use the override system (from what I have been able to see) and you are changing a core file.

Disclaimer:
I am currently testing this and so far find no issues.
While I have been a programmer for 25 years, I am new to ZenCart, php and SQL.

Jeff