PATA connectors looks like MOLEX in my power-supply-unit

"Molex connector" is actually a rather imprecise term, since the Molex company makes many, many different connectors. Including the main 24-pin ATX motherboard power connector! And companies other than Molex also make the connector you know as a "Molex connector", notably AMP but also many unbranded/generic ones are also available.

The 4-pin power connector that is commonly called a "Molex connector" is really more a general purpose peripheral power connector that delivers 12 V and 5 V power. It was most commonly used with pre-SATA hard drives, which are nowadays referred to as PATA (previously called IDE) drives.

Therefore, a power connector referred to as a "PATA" or "IDE" power connector is likely to be a "Molex 4-pin power connector" or "peripheral power connector" and looks like your latter pictures. Despite the different names, they are the same thing.

Your first pictured connector is actually a PATA/IDE ribbon data cable. Not power.

The ATX power supply specification actually refers (§ 4.2.2) to them as a "peripheral connector", specified as "AMP* 1-480424-0 or Molex* 15-24-4048 or equivalent". Note that AMP and Molex are two different manufacturers, and those are just part numbers.

Note also that the main 24-pin power connector (§ 4.2.1) is specified as "Molex* Housing: 24 Pin Molex Mini-Fit Jr. PN# 39-01-2240 or equivalent" -- another, different, "Molex" power connector.