Are sealed bearings equal to cartridge bearings in single speed hubs?
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: