Thanks for the part numbers, it looks like they’ve switched from using 24VAC contactors to 110/220V versions (depending on the part number you get), this allows them to drive the contactor with a line voltage and control it with a low power 24VAC relay (marked X within the drawing, kind that smart controllers will not have issue with).
Note: If the new relay would be able to handle the current needed by the pump (such as the relay from Orbit design), you would not need a contactor, since the relay alone would be enough. This is, in essence, the suggestion I’ve made to remove the contactor and use sufficiently large relay in it’s place.