Both of those words would apply to the dad in that example. Sure, you could qualify it as "primary caretaker" but that would likely be claimed by any person considering themselves "head of the family" whether they're the ones spending most time with the children or not.
The idea was to specifically include caretakers/guardians who are not parents (e.g. older siblings, grandparents or uncles/aunts) but also exclude those who do not take an active role (or take a less active role) in the actual caretaking. If my spouse does the brunt of all the caretaking, I may still be a caretaker or guardian but I don't need daycare in order to be able to work (though daycare may enable my spouse to work).
