Miracle worker uses the word "defeted". Does this mean you cant use it when somebody gets "wounded", ör is it the same thing?

RRG says:

When a figure has a number of damage tokens equal to its Health, the figure is defeated.

So yes, miracle worker triggers when a hero is flipped from healty to wounded.

"Defeated", RRG, Page 10:

When a hero is defeated for the first time during a mission, he is wounded and flips his Hero sheet to the wounded side. If a wounded hero is defeated, he withdraws and is removed from the map.