The little plug's are designed to plug into motherboard sockets,or headers as they're known,
the big ones are called molex connectors and are not usually anything to do with the Mobo (Psu direct line to the drive/fan etc), if there are molex and 3pin on the same line I'd say use one or the other,not both simultaneously,
if you use the 3pin, look for a header on the mobo you can use for it,
if you use the molex, just find a free line from the psu
Moto