It varies between different models. Some 970s require two 6-pin power connectors, some require an 8-pin and a 6-pin. Most 390s require an 8-pin and a 6-pin.
The 390 needs a 650w power supply vs a 500w unit for the GTX 970. AMD cards are not as efficient as Nvidia cards. The 390 needs an 8 pin and a 6 pin PCI-E cable and the GTX 970 needs 2 x 6pin connectors.
Edit: Sakkura is correct in that some models do vary based on factory overclocks. There are 970s that need an 8 pin and a 6 pin.
Not sure what that means. Both cards ( and all modern graphics cards ) use a PCI-E slot on the motherboard and supplementary PCI-E cables from the power supply. The 390 will need an 8 pin and a 6 pin connector. Most high quality power supplies capable of powering a 390 will have at least one and probably two 6(+2) pin connectors. The extra 2 pins are removable.
And just to be sure what is the make and model of the power supply?