It is distinct from water that later moved in from an aquifer or was injected. It is often nearly immobile, which is why it gets equated with irreducible water saturation, but the two words describe different facts. One is origin. The other is a flow endpoint on a capillary curve.
Calling all low water saturation 'connate' hides a transition zone, where the water is formation water that can still move. A water sample from a producing well may be aquifer water or injection water, not the water that was trapped with the oil.