In principle the sentence "Das Mittagessen ist fertig" could indeed mean "lunch is ready" and "lunch is over", but without context it would usually be understood as the former.
And particularly if you leave out the article (which in contrast to English is not the default here) it can only be understood as someone calling "lunch is ready/prepared!". (For a simple statement you need the article).
They might (or might not) be the same thing. This confused me too, so I looked it up.
Technically speaking, dinner is the largest (or main) meal of the day, and supper is the last meal of the day. So if the main meal of the day is the last meal then it is both / either supper and / or dinner.
If the main meal of the day is in the middle of the day and there is another meal in the evening then the first one (the main meal) is dinner and the second (the last one) is supper.
I put lunch is finished and got it right and the Translation also says lunch is ready. so which one is it. does it mean lunch is finished for the day or finished preparing the food ready to eat. Also I I am duel english and australian and was told growing up by Family and School that
Frühstück is breakfast
Mittagessen is lunch if it is not hot Food such as having Sandwiches for example or Mittagessen is dinner if it is a hot meal around midday
Abendessen is Tea if it is Food that is not heated or Abendessen is also Dinner if it is a meal that is prepared hot
Supper is what I know as a late dinner in the evening around 9pm and usually not as big as a dinner
Please refer to the lesson tips & notes for Duo's stance on this: https://www.duolingo.com/skill/de/Food/tips-and-notes