This is a fireplace and chimney system that was manufactured in a factory (as the name implies) out of metal. It is a modular system of component parts that was brought to a job site and installed once the wood framing for the house was in place. It has a firebox lined with refractory panels, with a damper at the top of the firebox and lengths of double or triple-walled chimney place on top to form a complete fireplace and chimney system. The chimney above the roofline may be enclosed by a wooden chase.
It has many slang names (which I refuse to use) but some of you may know this fireplace as a Z-Can, ZC, Zero Clearance fireplace (which is a misnomer) as clearances to combustibles are required. I’ve heard some people refer to it as an insert, which is totally incorrect.