Is an inference the same as a conclusion?

They are closely related, but not identical.

Inference = the process of reasoning from something you know to something you conclude.

Conclusion = the result of that reasoning.

For example:

Fact: Slavery was abolished.

Reasoning: If slavery is abolished, people can no longer legally be owned as slaves.

Conclusion: Former slaves were no longer legally slaves.

The inference is the reasoning connecting the first statement to the second.

The conclusion is the second statement.