Are sealed bearings equal to cartridge bearings in single speed hubs? Single speed hubs are often speced with sealed bearings. In my brief market search I haven't seen any hubs with cartridge bearings in the specifications.

Are sealed bearings used synonymous with cartridge bearings in the context of single speed hubs? How to identify if a hub has cartridge bearings?

In general, the presence of a seal does not depend on the type of bearing. A cup and cone bearing may be sealed while a cartridge bearing may lack a seal. However, track bikes (velodrome) usually have cup and cone bearings for adjustability and lack seals to reduce friction losses. This may have led to such hubs' bearings being referred to as unsealed.

See also a related question on hub bearings.
I'd take a cartridge to mean an entire unit, with bearings installed permanently and not intended for any servicing beyond a grease/lubrication.

A Sealed bearing would describe the seal around a bearing race, whether it be a ball bearing, a needle bearing or an angular contact bearing or whatever.  Some bearings are described as "shielded" or "double lip sealed" which adds drag.

Generally drag is to be avoided because it costs watts, but on your mud bike or commuter that's less important.  A track bike wants to minimise drag at all cost, and well-adjusted cup and cone bearings are perceived as lower drag than any sealed or shielded bearings. 

So IMO a cartridge bearing would be one that doesn't have loose balls, and the "sealed" bit means how resistant it is to water ingress.

Sealed cartridge bearing from a front wheel hub: