As stated above the disc plow turns the soil over while the harrow essentially breaks it up.
If you try to harrow a turf area you'll see the harrow will not penetrate very deeply into the turf so it requires lots of passes and even them will not do a great job. The turn plow, either disc type or moldboard type will invert the soil but commonly it will still be very clumpy so usually requires the harrow to come back over it and break it up and smooth out the surface for planting crops.
Some use a rotating tiller to accomplish the entire task but even then it can lead to a hard layer below where the tines can penetrate.
Not a farmer either but a pretty intensive gardener.
Bottom Plow
ETA to link video of a bottom plow