Translation:Cooks are cooking so that there is food for the families.
Damit and um...zu are Finalsaetze, they actually have the same meaning but the use is different, um ... zu must be used only with the same subject, with um...zu the conjugated verb is always in infinitv
Ich habe ein Auto gekauft, um (ich) die Arbeit zu gehen Er arbeitet so viel, um (er) seine Familie zu unterschuetzen
Damit can be used in the place of the um...zu, but it is not implied anymore that the subject is the same, as it is in this exercisie, the cooks are subject, and the families another, also the verb is conjugated normally.
I cannot understand why somebody downvoted your question. As we all know there are no wrong questions. You surely know that there is no distinction between "cooks are cooking" and "cooks cook" in German. Both can be translated as "Köche kochen". If your answer was not accepted by DL, there must have been other mistake in it.
Well let's just upvote it until it's back to zero. But maybe the downvotes were because "difference" was misspelled.
There is a distinction between "cooks are cooking" and "cooks cook" though not perhaps when considering both as present tense.
"Cooks cook" can also express a definition of what a cook does, similar to "fettlers do repair work on railways" or "aviators fly planes" or "anglers fish".
Maybe that's all a bit of a non sequitur ...