If you want to have website that display specific product and all the products, the sharing of VirtueMart will not allow that.
Such kind of things is possible with Hikashop that is enhanced with JMS multisite facilities.
Based on your requirement, you have to share the users between the websites because you want to have the users registered only once.
If the websites are on different domain name, you will need the additional "Single Sign-In for domains" extension to remain logged. Otherwise, the users will have to re-logiin with the same login and password.
The sharing of VirtueMart will result to have exactly the same product, categories, orders, ... in all the websites.
With Hikashop and JMS, it is possible to create Hikashop categories that are only available in specific websites.
As you can create product that are attached to several Hikashop categories therefore, you can attach a product to a specific website.
So this will solve your requirement concerning the same website with different products.
See our change history that explain that
www.jms2win.com/en/faq/change-history-13...d-hikamarket-sharing
Here it is also our hikashop partnership link
www.hikashop.com/download.html?partner_id=16361