What is the intuitive difference between $E(X 1_A)$ and $E(X|A)$?

Question

I know that they are not the same since $E(X|A) = \frac{E(X 1_A)}{Pr(A)} $ (*)

But without using formula (*) above, for me, both of them means "Average of X on an event A".

Could you please explain for me intuitively what is the subtle difference between $E(X 1_A)$ and $E(X|A)$?

Thank you.