Okay, for the benefit of this and future generations, herein a short history of cross country bindings.
In the beginning, Lapps created the toe strap a few thousand years ago. It is rumored that this device persisted even into the middle of the 20th century among certain Scandinavian-American enclaves. (Sure wish I'd had the foresight as a kid to hold onto some, until the advent of eBay and the nostalgic urges among some restaurant and lodge owners . . . )
The toe strap begat the toe and heel strap in the mid 1800s, in which tension around the heel kept the boot in the binding. The toe and heel strap evolved into a metal cable attached to a metal toe piece. (Believe it or not, these latter bindings were also used on downhill/Alpine skis for many years, keeping entire armies of orthopedic surgeons gainfully employed.)
In 1927, a Norwegian skier/inventor named Bror With showed up at a ski race with a pair of bindings he had designed. They featured a bail that locked over a lip on the boot and three pins that fit into holes on the soles under the toes. The crown prince of Norway was in the race and asked him what that was on his skis. With replied, "Oh, these are just some rat-traps that I made," and an empire was born. Rat trap in Norwegian is "rottefelle" ("rottefella" in the definite form.)
The Rottefella binding design ruled the roost for the next fifty years among cross country types. Sometimes they were sold with cable bindings, sometimes not. Until the industry settled on one standard width of 75 mm several years ago, the Rottefella-type bindings were sold in various widths to accommodate different boot sizes.
The 75 mm sole width (aka "Nordic Norm") now appears in all "three pin" binding systems, whether they include heel cables or not. The 75 mm width standard was also adopted for the "free heel" telemark bindings that started appearing in the 70s, but these don't always incorporate the three pins.
The NNN ("New Nordic Norm") and SNS ("Salomon Nordic System") are "newer" binding types that use a metal rod imbedded across the toe end of the boot sole. This rod clips into the binding, providing a somewhat different flex and control than the three pin system. NNN bindings fit only NNN boots, and SNS bindings fit only SNS boots. If you're shopping for either of these binding systems, you pick your boots first to make sure you can get a good fit, then you take your pick among the compatible bindings. NNN and SNS bindings come in different flavors for different skiing types. The "BC" designation on some of them indicates a wider, beefier construction for backcountry use. BC versions will not work with ordinary NNN and SNS versions, so make real sure your boot fits your binding.
Things were too simple -- the public was actually starting to understand the nomenclature -- so a conspiracy arose to promote the mysterious, long-promised "New Telemark Norm" NTN binding and boot system. Rottefella teased skiers for several years with this, and it's finally on the market. Black Diamond wanted to make sure that consumers would spend more time reading about binding systems than actually skiing, so they came up with an entirely new system very recently.
Sigh.