I am pretty sure that an app is per domain (ie. VS) because each domain uses a webserver. so presumably will use its own chunk of memory & operational processes on the box (VM). I would also think it would be very odd to have multiple domains using exactly the same app (ie same users, same data, etc)
Unless you’re using the multi-site WordPress variant (which I can’t recommend for most folks), you have an independent installation for each one.
That said, “resources” is a tricky topic. As long as you’re using the same version of PHP across all of them, many of the memory pages will be able to be shared whether you have one or one hundred WordPress sites (Linux has quite advanced memory management, including tactics to share memory in cases where pages are identical). The more of the same application you run, the more efficiently each one will run, though overall system usage obviously still goes up as you add more sites.
But…on the other hand, the database is always the bottleneck and the biggest resource user, and those can’t be shared, even in a multi-site configuration (you don’t want users for one blog to be able to modify the others, for example).
So, the short answer to your question is: It doesn’t matter. There aint no such thing as a free lunch. You pay a resource cost for each WordPress blog whether the installation files are shared or not. Realistically, only disk space can be saved by having a multi-site WordPress instance, and disk space is by far the cheapest resource available. You shouldn’t really be trying to optimize for disk space, because memory and CPU and disk speed will be your bottlenecks.