What is the difference between palm tree and coconut tree?

Yes, they are the same thing. The coconut palm tree is a generic name for the palm tree species. There are many kinds of coconut palm trees, but the most famous ones are known as the Malayan Coconut Palm Tree and its Scientific name, or botanical name, is Cocos nucifera.

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I placed a link below that talks about the Malayan Coconut Palm Tree in more detail.