One aMember license can be used on one domain only(and on all subdomains within this domain). So you have to purchase additional licenses if you want to use aMember on multiple sites.
Two site that do not share products? Two sites, same server, same SQL server I want one site to display one set of products and another site to display another set, Plugins, payments, users etc all the same.
You can do this using price groups. Just set different negative price_groups for products on different sites, so for example: /amember/signup.php?price_group=-1 will should products for site one /amember/signup.php?price_group=-1 will should products for site two