Can someone explain me the PCI-E slot variations & sizes

pcie slot length   Dan pcie 4 in pcie 3 slot

Verilux® NVME Adapter PCIe x16 with Gel Pad, NVME or AHCI SSD to PCIE Adapter Card for Key M 2230, 2242, 2260, 2280 Size SSD, Support PCIe x4 x8

I don't think he's concerned about just the full length ports but the half slots that are sprinkled between the full-size slots, those tend to PCIe x1: These are the smallest PCIe slots, used for almost any other cards like average network adapters and USB expansion cards · PCIe x4:

slot gaxor It is only 130x31x10mm in size and when seated in the PCIe slot it only stands up by 23mm With the small size, it is capable of holding the longest M  PCIe Slots · A PCIe slot that supports a full-height full-length PCIe card also supports a full-height half-length or half-height half-length