At first glance, targeting site ID 8-96824 (site name "weather.com") appears to be the same as creating a domain whitelist with the domain "weather.com" in it. There are significant differences however.
Exchanges usually organize their inventory by site ID. These IDs represent specific "sites" that have been set up with the exchange.
In many cases, a "site" corresponds to a domain name, however under some circumstances, a "site" can contain many different domains. For example, some sellers on an exchange choose to bundle many different domains in one site ID; a common case is an ad network that is using an exchange to fill unsold inventory. For example, see 3-38945 ("coxdigitalsolutions.com").
We attempt to provide the best name possible for a site ID. If we detect there are multiple domains in a site ID, we will give it a name as descriptive as possible of its contents, such as the domain of the parent publisher (for example, the site called "glammedia.com" contains inventory from across Glam Media's network). If we do not have a descriptive name available, we will label it generically as a "Site Bundle". Some publishers prefer to sell their inventory anonymously and we will not be able to display a meaningful name or any meaningful domains in this case.
We are not always able to detect the presence of multiple domains ahead of time in a site ID, but attempt to do so wherever possible.
Targeting by selecting sites from the inventory tab tells our bidders to bid on all impressions with the site ID in the bid request; remember, we show a "site name" for your convenience but the bidder is acting on the underlying site ID.
On the other hand, targeting by using a domain whitelist tells our bidders to bid on all impressions where the domain name is observed in the bid request; site ID is not taken into consideration.
In campaign detailed reporting, the report is organized by site but you can see the additional domains, if any, by selecting the "(more)" link beside the site name.
There are merits to both the strategy of selecting by site and buying using a domain whitelist.
If you absolutely only want to buy impressions on specific domains, it is best to use a domain whitelist. You may also be able to reach more inventory if some inventory for a domain is found in one of the bundled sites.
On the other hand, the nature of how the inventory is organized can sometimes indirectly reveal information about quality. When inventory is available as a named site, it often means that the site works directly with the exchange, and the impressions may be higher in the impression stack (given higher priority in the publisher's ad server when determining what ad to show users). Inventory that is found inside a bundled site ID may be more indirectly sold; the site may be working with an ad network which is working with an exchange. In this case, the impressions may not be as high in the impression stack; the publisher may only serve this when they have exhausted all higher-paying options such as directly sold campaigns and direct exchange integrations. This is not a firm rule, however.
Testing both methods will give you the most insight into what tactic works best for you.