Wood – use an “impact driver for concrete” to drill or drive screws in wood

Most driver bit sets come with a 1/4" square drive adapter (my small Milwaukee set also came with a 3/8" drive as well, though I don't know if that's common). With that one bit, your driver is instantly almost exactly the same as a 1/4" impact wrench. You'd have to look at torque specs to see if the models you're considering are comparable, but I bet they are. Those little impact drivers have come a long way -- battery life is great and the torque is hard to believe.

I'd only consider a square drive impact wrench for heavier automotive (or other mechanical) use, and only in a larger size like 1/2" so it can provide some real help in removing tough fasteners.

Drills and impact drivers are similar in that they're both rotating power tools and they have some overlap in usage, but they work differently and have different strengths.

Drills apply a constant torque and tend to have good control across a range of speeds and clutch settings. They're good for work that requires care or precision, like drilling a hole or driving a a smaller screw.

Impact drivers provide much higher torque but in rapid bursts–very much like a hammer provides bursts of linear force. This makes them good for heavy-duty jobs like driving long lag bolts (you can even take the lug nuts off your car wheels with most impact drivers), but the banging action makes them a little bit difficult to control. They're also not good for driving into something very soft–between the hammer strikes there's no torque applied and the bit can actually rotate backwards. You can see this by holding the chuck with your hands while the driver is on; you'll feel the pulsing of the strikes but chuck won't actually rotate. Finally, some impact drivers don't have a clutch, which means you need to be very careful if you're driving something that could be over-tightened or broken by the high torque.

Besides the higher torque, impact drivers have another huge advantage in that you don't have to hold them tightly to provide the torque. The momentum of the rotating striker inside is what provides the rotation force, so even when you're driving something very tough it's quite easy to hold the tool. Drills on the other hand provide a constant torque and require the user to provide the reaction and prevent the tool from spinning.

If you have to pick a single all-purpose tool for general DIY use, a drill is much easier to control and is useful in a wider range of situations.