I see the term 'factory built wheels' all the time, but I have no idea what they are, how to recognise them, what's different about them as compared to hand built wheels, other than the obvious (made in a factory, but even that is pretty nebulous).
I'm not sure there's a formal definition, and there are probably grey areas over which wheels are which - I've got some old Tecno ones that are pretty borderline. But, in general terms, traditional wheels are built up from hubs, spokes and rims that may be sourced separately, from different manufacturers, and are quite interchangeable. The actual building may, of course, vary from hand-built by a specialist such as those mentioned here, to mass production in a factory.
"Factory" wheels still usually have hubs, spokes and rims. However, they are designed as single entities, so that the rims and spokes are typically made just for that particular wheel or range of wheels. They may use very small numbers of spokes (perhaps 16, where hand-built wheels are considered ultra-light at 24), and unique lacing patterns. If a spoke breaks, then in many cases (but not all), you're not necessarily just intended to replace it. It may be a case of return to the factory for repair, or replace the wheel. Spokes may screw into the hub or use other proprietary fitting methods, whereas traditional wheels have spokes with bends and heads, that fit into standard drilled holes in the hub flanges.
Factory wheels tend to be lighter than traditional ones, but may not be as durable, nor (see above) as easy to maintain. They can, in some cases, also be phenomenally expensive. So you takes your choice.