I'm Jason a Guru here at Shopify.
It would be possible to open two different stores, one under www.example.com (for example), and the other at its subdomain, example.mystore.com.
Also, to make sure that this is clear, you'll need to operate these separately on two separate Shopify accounts!
In terms of how to set this up, it does depend slightly on whether or not you purchase the domain from Shopify. If you purchase the domain for store #1, you'll then add this subdomain as an existing domain in store #2, both cases within Online Store > Domains.
Although currently, it is not possible to run multiple stores under one account/admin, it is possible as I mentioned to have two different stores under one Domain, having the second as a Sub-Domain!
You can add multiple Domains to one store and have them all redirect to the same place - but if it's going to be a different online storefront, with different suppliers/warehouses/products/etc, then you'd need an entirely separate account.
I hope this helps, let us know if there is anything else we can help you out with! - Jason
Just saw your reply and noticed a mistake: You wrote "It would be possible to open two different stores, one under www.example.com (for example), and the other at its subdomain, example.mystore.com."
A subdomain always appears BEFORE the main domain, e.g. mystore.example.com and not example.mystore.com as in your example, which would be correct if mystore.com is the main domain, and example is a subdomain.
|an hour ago|
|an hour ago|
|2 hours ago|
|3 hours ago|