"Today we make them with other tools."
Translation:Dnes je vyrábíme jinými nástroji.
The preposition is not included in the main translation above. Perhaps your answer was sufficiently different from what DL expected that it gave you a "correction" that was more in line with what you wrote. When you have a question about something weird like this, it's helpful to the Czech team if you paste your actual answer into your comment.
My guess would be that další wouldn't work here, unless the sentence can also mean that "we make them with ADDITIONAL tools" (as in, tools in addition to the ones that were used in the past). My immediate reading of the sentence goes to "different/jiný," but perhaps the "additional" context would also be acceptable. If is is, I will add translations using další.
jiný - muu, eri, erilainen
další - seuraava, lisä-, muu
"erilainen" is also "odlišný" or "rozdílný", and "seuraava" is also "následující" or "příští" (These longer words and more specific). Your problem is, obviously, that "muu" is usually "jiný", but can sometimes be "další" in Czech. Then you have "toinen", which is often "druhý", but it could also be "jiný" in some situations. Hmm, I thought I'd give you a clearer answer, but now that I'm writing it, it seems more complicated. It would help to use a lot of examples I guess.
The main theme of "jiný" is difference - something is not the same as something else. It's slightly in the direction of "strange", "unfamiliar". On the other hand, "další" is related to "dál" (further, on, onwards), so it can be: another (more), additional, further, next, extra, following.
Sometimes the meaning is sort of in the middle and can be expressed by both words, for example: "Muu ei tullut edes mieleeni." - "Nothing else even occurred to me." - "Nic jiného mě ani nenapadlo." (I didn't have a different idea, only the one mentioned previously) or "Nic dalšího mě ani nenapadlo." (I only had that one idea mentioned previously, no more ideas on top of that) - here the meaning is very similar.