How are premises and conclusions different from assumptions and implications?

I was talking to chatgpt about logic and how it works. This question arose since in natural language premises and assumptions are similar, as well as conclusions and implications. These concepts are used in specific ways in logic. I thought the AI gave useful explanations and examples as to how they are different. More could be said about implication though.

In a logical argument, the premises are the reasons or evidence that are offered to support the conclusion. The conclusion is the main point or claim that the argument is trying to establish. The relationship between the premises and the conclusion is that the premises are supposed to provide evidence or support for the conclusion.

In contrast, assumptions and implications are not directly part of the argument itself, but are related to the argument in other ways. Assumptions are the background beliefs or conditions that are necessary for the argument to be valid or reasonable. Implications are the logical consequences or implications of the argument.

For example, consider the following argument:

Premise: All dogs are mammals.

Premise: Fido is a dog.

Conclusion: Therefore, Fido is a mammal.

In this argument, the premises are "All dogs are mammals" and "Fido is a dog," and the conclusion is "Fido is a mammal." The relationship between the premises and the conclusion is that the premises provide evidence or support for the conclusion.

Now suppose that one of the assumptions of this argument is that "mammals are a type of animal." This assumption is not explicitly stated in the argument, but it is necessary for the argument to be valid. Without the assumption that mammals are a type of animal, the conclusion "Fido is a mammal" would not be meaningful or relevant.

Finally, suppose that one of the implications of this argument is that "Fido is not a reptile." This implication is not directly stated in the argument, but it follows logically from the premises and conclusion. If we accept the premises and conclusion of the argument, then it logically follows that Fido cannot be a reptile, because reptiles are not mammals.

In summary, the difference between premise and conclusion vs. assumption and implication is that premises and conclusions are directly part of the argument, while assumptions and implications are related to the argument in other ways. Premises provide evidence or support for the conclusion, while assumptions are necessary for the argument to be valid, and implications are logical consequences of the argument.