Call/put option formulae and physical interpretation

I'm revisiting this exam having taken CT8 quite a while ago - at the time I took an ActEd tutorial at which I recall the tutor really helpfully identifying what the different parts of the equation correspond to. It was something like (e.g. for a call)
ct= (St component: share price with the probability that it'll move interestingly) - (K component: strike price discounted, also adjusted by some probability term).

Following on from that, I suspect these go on to have a physical interpretation in terms of the replicating portfolio of the option.

Unsurprisingly, I only vaguely recall this and I think it's a) not in the notes, b) has been the key to answering an exam question before.
Has anyone come across this and know the interpretations?

 

Helpful update for the internet:
K component corresponds to present value of a fixed payment of K (either to or fro, depending on call/put) at time T, depending on the value of underlying share price St. This came up in CT8 S11 Q8. Among other places.