All that we can see in the picture is the discharge side of the pump. 3/4 and 1/2" would be expected here.
You need to follow the intake piping. It will take you to the well cap (if there is one).
Is there a tank in the lower right of the photo?
These things can run for a long time before the pump cycles.
What is the elevation of the house compared to the water supply (if no well cap found)?
Booster pumps are found in houses where the house is up there with the public water tanks.
If you find a lot of these in your area, you may consider the “Well & sampling course”