According to your description 'Tarinat' seems to be a direct translation to 'Created by'. Remember direct translation don't have to be word by word translations. It only matters that both role names describe the same function.

Quoting Kulju:

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I think that it's correct to change Timo Varpio's Käsikirjoitus credit from Screenwriter to Writer on second season since there isn't Story by credit anymore, so we can assume that he have written the stories too. In finnish language we don't have different words for Writer and Screenwriter in this context. It's always Käsikirjoitus.

I don't think we can assume that as a 'story' isn't required.  It is possible, even normal, to just write the screenplay directly.  If it is 'Screenwriter' in the first season, I would leave it as 'Screenwriter' for the second as well.

Now I remember where I got my idea how to translate credit Käsikirjoitus/Käsikirjoittaja (Writing/Writer) in context. It's straight on the program menus. If you go to edit mode and select for example screenwriter there is a clarification below "Screenwriter: adapted screenplays" for writer you get "Writer: written directly for the screen".

Quoting TheMadMartian:

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A writer is the person who is responsible for both the story and the screenplay.

Yes, I agree and therefore the correct credit in this case is writer.

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The absence of a Story by credit does not, however, automatically make the screenwriter a writer.  There could still be material, of a story nature, that the screenplay was based on, just no credit given.

But that would require inventing story by credit which is not there. I was under the impression that we don't invent something that is not in credits.

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Since the translation can go either way, without knowing for sure, I don't think we can assume.

It's more than assumption. If there is only one writing credit it has to be writer.

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If there is a story by credit, there can't be a writer credit, it has to be screenwrite

You are correct but it also goes other way around. If there is not story by credit, it has to be writer.

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Please note that my opinion is based on Hollywood credits, if Finnish credits are structured differently, I will concede the point.

They aren't that much different. Only problem comes due the translation cause you guys have two different words (Writer/Screenwriter) where we have only one (Käsikirjoittaja). You must check all writing credits to deside which is the correct translation case by case.

There are even more difficult credit to translate and that's Art Director / Production Designer and that's due the differences how films are made here compared to Hollywood. Again we have only one word for that role (Lavastaja) which can be one or the other or neather or something between I usually translate his role as Art Director.