PC Hardware → connect to PSU, Mobo?

I have a couple of case fans that have these 4 pin connectors which can plug into one of my PSU power cables and 3 pin ones that can go onto motherboards. Do they both need to be connected?

Thnks.

No, either or. If your motherboard is older than 2 years or so, use the 4-pin connector - the 3-pin connectors on older motherboards couldn't handle a fan that drew more than 2 watts or so.