When I search both online I get the same definition of to struggle.
What is the different use of them then if the meaning is the same?
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奋(to erect) 斗 (to fight)
奋斗 (summon up all of one's will and strength and fight) = to strive; to struggle (metaphorically)
挣 is a pulling motion, 扎 is a thrusting motion
挣扎 (pull and thrust) = to struggle (graphic description of a physical struggle or metaphorical expression of desperately trying to break free from a situation
奋斗 and 挣扎 are both intransitive verb. 奋斗 has the meanings of 'fight hard/ work hard' and 'struggle'(metaphorically)
挣扎 also means 'struggle'(metaphorically or physically) , but it express a stronger sense of 'desperation'.
We can describe an animal get trapped in a net, struggles to break free as 挣扎, but we cannot use 奋斗 to describe this physical struggle
We can describe a person’s struggles to advance in the society with either 挣扎 or 奋斗, (挣扎 expresses a more desperate manner)
這局棋已經無望了，但他仍在苦苦挣扎 - This game is already hopeless, but he is still desperately struggling (to escape defeat)
雖然十年未奪得頭銜，但他仍在努力奋斗 - Although he hasn't won any title for ten years, he is still working hard and striving (to win one)
奋斗：to make a great effort to achieve something, usually striving to be successful. It's a positive word, because you have a target to achieve.
挣扎：try to struggle (to get free), usually we say someone is trapped by something bad, and try to struggle from it. It's much more passive feeling, because you have to struggle in order to escape from something bad to you.
See these expressions:
Well, I often hear 努力奋斗 in speeches by 习近平 and other 党员们
I don't hear 努力挣扎 so much.
I think they are not the same. When you strive, 奋斗, you want to be better, improve something.
When you feel threatened, you may struggle: 不要挣扎了。 Don't fight it. (you won't achieve anything)