PCI and PCIe are two very different interfaces, they are similar in name only.
The possible PCIe lane configurations are dependant on the physical connections.
Most modern Intel motherboards have one to three PCIe 16x slots connected to the PCIe lanes exposed by the CPU itself. There are 16 PCIe lanes on each of the LGA-1156, LGA-1155, and LGA-1150 socket CPUs. These can be configured in 16/0/0, 8/8/0, and starting with IvyBridge 8/4/4.
Intel chipsets also expose an additional 8 PCIe lanes from the chipset. These are used for peripherals such as network adapters, audio codecs, bluetooth adapters, etc... There are also often one or more PCIe slots exposed from the chipset lanes, commonly 1x, 4x, or a 16x wired in 4x mode.
A 16x slot...