What is the difference between a PC, APC and UPC  finish on a fiber optic connector and why would someone want to use one verses the other?

Whenever a connector is installed on the end of fiber, loss is incurred.  Some of this light loss is reflected directly back down the fiber towards the light source that generated it.  These back reflections, or Optical Return Loss (ORL), will damage the Laser Light Sources and also disrupt the transmitted signal.  To reduce back reflections, we can polish connector ferrules to different finishes.  A typical hand polished connector will measure at -30dB.  This polish is referred to as a PC or Physical Contact polish, which for some systems is considered too high of an ORL measurement.  To reduce the back reflection of a connector, we can machine polish it to SPC (Super Physical Contact) polish or UPC (Ultra Physical Contact) polish.  Industry standard is a minimum of -40dB for SPC Back reflection measurement and -50dB for UPC back reflection measurement.  If even less back reflection is required, an APC, or Angled Physical Contact polish, might be necessary.  An  APC connector has an 8º angle cut into the ferrule.  These connectors are identifiable by their green color.  An APC polished connector has an Industry Standard Minimum f -60dB ORL measurement. Abroad most CATV and telephone companies require the use of these low back reflection connectors. PDR has the state of the art technology and equipments to produce higher standard Super, Ultra and Angled patchcords. PDR assemblies are prepared by highly skilled technicians and each assembly is checked to guarantee highest performance.

When we speak of dBm (decibels to a milliwatt) we are measuring absolute power. For example 10dBm equates to 10 milliwatts, watts being a power denomination we recognise. True loss of a signal or the difference in dBms, is expressed in units of decibels, commonly abbreviated as dB. Fiber attenuation and connector loss are generally expressed in units of dB. As an example, singlemode fiber loss may be expressed as .3dB/km and a connector loss may be .2dB. In fiber optics the negative sign (-.2 dB) is generally ignored.

What is the difference between Singlemode and Multimode Patchcord and why would someone want to use one verses the other?

All fiber consist of a light carrying core in the center covered by an optical coating called cladding that traps light within the core. The difference between multimode and singlemode is the diameter of the fiber core. The core diameter is either 50 or 62.5 micron for multimode and 9 micron for Singlemode. Multimode patchcords are primarily used with LED sources for LAN and security systems. Its large core makes it easy to couple lots of light from inexpensive LED's and it has adequate bandwidth for most premises applications. 
Singlemode patchcord has higher bandwidth and low attenuation because of its smaller core. But the smaller core needs expensive laser sources for efficient coupling, generally limiting its use to very higher bandwidth system used over long distances. Telecom and CATV system all use singlemode patchcords. Built to your specifications multimode and singlemode patchcords are available from PDR in simplex/Duplex style. All PDR patchcords are tested utilising the industry's latest equipment and offer superior quality at low prices on all style of patchcords. PDR patchcord represents high quality, very loss and maximum performance. Singlemode Patchcords have yellow colour jacketing and multimode patchcords have orange or grey colour jacketing.

The most visible difference between the two adapters is color. Most singlemode SC/PC adapters are blue and SC/APC adapters are green. This allows for quick identification, especially when used in distribution panels so the end-user inserts the correct connector type. Often users cannot see the connector plugged in on the backside of the panels, therefore the color indicates the SC connector that's required. SC connectors correspond with the adapter; most singlemode SC/APC connectors have green outer shells while singlemode SC/PC connectors have blue outer shells. SC/APC adapters use premium zirconia split sleeves to achieve the tightest tolerance possible providing critical alignment of the two angle polished ferrules. Whether it is a singlemode SC/PC or SC/APC connector be sure to choose a zirconia (ceramic) sleeve material rather than a phosphor bronze or polymer. The zirconia alignment sleeves have a tighter tolerance and better elasticity, maintaining tight tolerances after several matings.