Molex originated a large variety of connector types, but only one is commonly used in microcomputers, and thus known unambiguously as a "Molex connector" in that context. An AT or ATX standard power supply normally has multiple connectors of this type.
The four pin peripheral power cable dates back to the original PC. It was used for floppy drives and hard disks. It's still around and is now also used for all kinds of things including add-on fans, extra video card power, supplemental motherboard power, and case lighting. It's as old as the hills but is still very widely used. The connector is shaped so that it only fits in one way. You don't have to worry about inserting it the wrong way. People often use the term "4 pin Molex power cable" or "4 pin Molex" to refer to a four pin peripheral power cable. It's not a technically useful term because the 4 pin 12 volt cable is also a 4 pin Molex cable (Molex makes lots of connectors) but "4 pin Molex" is commonly used to refer to peripheral cables anyway.