"Nevertheless" is more commonly used when saying 'A' happened despite 'B' where 'B' is something negative, or something that might normally stop you from doing 'A'. Similar meaning to "even so" or adding "anyway" at the end of a sentence. Example: "It was raining. Nevertheless, I went to the park." "It was raining. Even so, I went to the park." "It was raining, but I went to the park anyway." All three sentences mean the same thing.
"However" is sort of the opposite and is usually used to say that 'B' succeeded in preventing 'A'. Example: "I was going to go to the park. However, it was raining, so I stayed home." "However" can also be used like "nevertheless" if you add "anyway". Example: "It was raining. However, I went to the park anyway." In this case, 'I' succeeded in preventing the rain from stopping 'me' from going to the park.
I can see how the difference can be confusing so let me know if you still don't understand.
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