First thing to remember is that the companies (Apple, HTC, Motorola, even Samsung to some degree) don't actually manufacture their parts. They hire a mass manufacturer to make and assemble their screens, then the screens are shipped to the actual Apple/Motorola/Etc assembly plant.
The 3 major grades of all phone parts are as follows:
OEM: Manufactured and assembled by the same manufacturer that produces for the assembling company. For example, Apple hired FoxConn to produce the screens for the iPhone 6 series. A screen manufactured and assembled by FoxConn, and just never sold or sent to Apple is an OEM. These parts are available on the retail market for select distributors. These parts are never manufactured in the US. They all come from China.
Recore/Refurb: Original LCD/Digitizer reman'ed using an aftermarket glass and possibly frame. There are hundreds of small companies doing this.
Aftermarket: Manufactured and assembled by a 3rd party company. Usually on the cheaper end of the market due to the 3rd party company shaving costs. Example: Using hot press glue to stick a screen into it's frame instead of cold press glue (hot press is cheaper, but loosens when the device gets too warm).
To circumvent problems with contracts/copyrights here's how it works. Apple calls up an end manufacturer (let's call this entity 'Parent') and signs an exclusivity agreement for production. Apple orders 100k screens. Production company has 3 sister production facilities to accommodate timeframes. Let's call them A, B, and C respectively. The contract stipulates that facility A will produce the order. So, Parent instructs A to produce 150k screens (extras for bad screens, warranty, replacements, etc). After Apple picks up and is happy with their order, Parent still has, say, 10k screens at facility A. They send those screens over to facility B, have the logos either smeared, covered, or removed, and they resell them on the retail market to select distributors. They then filter onto our market. Manufacturers in the US have been doing this behind the scenes for decades.
The hardest part is getting the original parts here in the US. Because of copyright laws, companies like Apple and Samsung have been bullying small repair shops around the US for not paying 'royalties' on the original parts. I've been purchasing direct from China for over 2 years, and I can guarantee you the screens I put into an iPhone or an iPad are the exact same as the ones Apple purchases for the same.