Why is inference different in logic and statistics? In Bayesian Inference, the term "inference" means learning parameters. In logic, inference means deducing something. Why are these two terms different?
 A: Statistics uses inductive inference while logic uses deductive inference.
If you've taken a logic class, you likely know about syllogisms.  For instance

All men are mortal
Socrates is a man
Socrates is mortal

This is an instance of deductive inference; If the premises are true the conclusions must be true.  However, in statistics (well...empiricism in general), we are never really aware of the truth value of any statement.  Statistics and science is full of assumptions, and so we can't do inference in the same way I've shown above.
To your question, why are these two different?  Logical/deductive inference allows us to arrive at true conclusions from true statements.  In Statistical/inductive inference, we do our best given our circumstances to arrive at true conclusions, but any number of things can make our inferences wrong.
A: The general English meaning is pretty broad

a belief or opinion that you develop from the information that you know

In both cases, logic and statistics, broadly speaking, it’s about “learning” something. Sometimes different disciplines just borrow same words from common language.
A: I like this example from Cohen (1994):
Logic:
Premise: If a person is a Martian, then he is not a member of Congress. (True, right?)
Data: This person is a member of Congress.
Conclusion: Therefore, he is not a Martian.  (Correct by the laws of logic: $M \Rightarrow \neg C \Leftrightarrow \neg\neg C = C \Rightarrow \neg M$). 
Probabilistic counterpart:
Premise: If a person is an American, then he is probably not a member of Congress. (True, right?)
Data: This person is a member of Congress.
Conclusion: Therefore, he is probably not an American. Nonsense, ignores baseline that there are very few members of Congress.
