딱딱하다 하고 단단하다 뭐가 달라요?

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딱딱하다 is when something is texturally hard
단단하다 is more like something is very solid and firm

Also 딱딱하다 generally gives a negative nuance while 단단하다 in many cases have positive, complimentary nuance to the object it's describing.

딱딱하다 can also be used on non-objects.
For example
말투가 딱딱하다= The tone of the speech is hard (in this case it means not friendly)
움직임이 딱딱하다= The movement is hard (as in it's not flexible)

I think 단단하다 has a broader meaning as in "something that doesn't easily change from outside forces"
For example, 나사 풀리지 않게 단단하게 조여라
-> Make sure to tighten the screw so it doesn't get loose
(단단하다 is used in this example because the screw doesn't change [get loose] easily)

You can use 단단하다 to describe someone's unchanging will of iron or determination
-> 그는 단단히 결심했다.