What is the difference between them?
What is the rule for usage of them?
Are they the same?
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Perhaps you could give more complete examples.
"I'd like to ..." could be followed by a description of something that you would like to do. For example, "I'd like to swim the English Channel."
It could also be a response to a question about things that you have done, to express the idea that you have not done it but want to. "Have you ever swum the English Channel?" "No, but I'd like to." Or it could be a positive response to an invitation. "Perhaps you and I could swim the English Channel tomorrow?" "Oh, I'd like to."
"I'd like that." is a complete sentence. It means essentially the same thing as my last example above. "Perhaps you and I could swim the English Channel tomorrow?" "Oh, I'd like that."