Molex and Sata
No because they have different connectors.
The number and type of power connectors provided by a power supply can vary widely depending on the model. Common types include 4-pin Molex connectors, 6+2 pin PCIe connectors for graphics cards, SATA power connectors for drives, and 24-pin ATX connectors for the motherboard. For instance, a typical power supply might provide three 4-pin Molex connectors, four SATA connectors, and two 6+2 pin PCIe connectors. Always refer to the specifications of the specific power supply for accurate details.
You can get a power supply tester on ebay for $5. It will test all the connectors.
Computers
If it as a 20 or 24 pin connector and a 4 pin connector then it is a ATX power supply.
SMPS
AT Power Supply - still in use in older PCs.ATX Power Supply - commonly in use today.ATX-2 Power Supply - recently new standard.
it can simply be called a "power supply" or a PSU (power supply unit)
Most often, power supplies for any type of equipment is givin to you when you buy what the power supply is for.
TRUE
Computers require their own internal power supply because the power required to power most newer computers, especially with high-end graphics cards, would require a bulky power supply which wouldn't be ideal in transporting computers or aesthetically. Also, with all of the other internal parts of a computer, some type of power interface would be necessary within the PC anyway, so why not just bundle it all together?
Electrical devices such as plugs, connectors, or cords are typically attached to a receptacle for power supply purposes.