I wouldn’t get too bogged down with the minutiae of these. I would just know that the ex-ante IC uses the correlation between your projected active returns and actual active returns.
The ex-post IC is the correlation between your actual active return and the expected active returns. In all the IC measures your skill. ex-ante these are always positive (you are always projecting a high correlation between what you say will happen and what actually happens) but ex-post these tend to be small if not negative (in reality there is little to negative correlation btwn what you said was going to happen and what actually did).
You can get bogged down with the formulae and the risk weightings, etc. but in my opinion if we run into a question about calculating IC then just mark B and move on.