All addresses managed by a DHCP server are considered part of the "pool". The IP addresses may or may not be contiguous, and multiple IP ranges may be configured. This is a server defined implementation detail. Once a DHCP server is running on a network, it owns the IP ranges which it is configured to assign. Any other configuration is an error, or undefined.

Addresses are either assigned via automatic allocation or manual allocation (e.g. DHCP reserverations/static leases).

The reason you generally see only a simple range of IPs in consumer routers is that it makes the UI easier, and its easier for consumers to manage.