Ethernet is point-multipoint network (multiaccess) and there is more than 2 routers.

OSPF elects a DR to be the focal point of all link-state updates and LSAs. The role of the DR is critical, therefore a BDR is elected to "shadow" the DR. In the event that the DR fails, the BDR can smoothly take over.

Serial is point-to-point access and don't need elect a focal point for updates.

Disclaimer

The Author of this posting offers the information contained within this posting without consideration and with the reader's understanding that there's no implied or expressed suitability or fitness for any purpose. Information provided is for informational purposes only and should not be construed as rendering professional advice of any kind. Usage of this posting's information is solely at reader's own risk.

Liability Disclaimer

In no event shall Author be liable for any damages wha2tsoever (including, without limitation, damages for loss of use, data or profit) arising out of the use or inability to use the posting's information even if Author has been advised of the possibility of such damage.

Posting

OSPF uses DR/BDR if there's a chance for more than two OSPF devices on media interface.  Ethernet commonly supports multiple devices 'visible' on the same interface.  Serial interfaces generally only have one device "visible" on the interface.  So, OSPF defaults to multi-point support for Ethernet and p2p for serial interfaces.

However, there are exceptions, and then OSPF can be reconfigured to override its default assumption.  For example, an Ethernet link used with a /30 or /31 for a p2p between a pair of OSPF devices.