The difference between the two words is subtle. However, "collaborate" has another meaning which is negative. See meaning #2 under "collaborate".
Working or acting together for a common purpose or benefit. (為了利益而) 聯合; 合作
The students cooperate to complete the tasks. It merely means working together to get something done. We can cooperate, but not collate as we may 各懷鬼胎.
1. Working as a team, contributing in a joint intellectual effort. (同心協力) 合作
2. Colluding as traitors, providing all information to the enemy. (與敵)共謀
1. John and Mary collaborate in the science project. They contribute their knowledge and work together in solving problems and creating the best science project ever for the science fair. Here, collaboration involves trust and knowledge sharing.
2. Mr. Ma collaborates with Communist China by selling out Taiwan’s sovereignty, in hope of securing a political seat in China in the near future.
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