With all of them you can calculate the impact of 1t of pig iron, the life cycle modeling is different in APOS, cutoff, and consequential, and LCI means aggregated processes while upr means unit processes. APOS, cutoff and consequential are the ecoinvent system models, which are explained here: https://ecoinvent.org/the-ecoinvent-database/system-models/
In short, APOS links to previous and next life cycles, while cutoff "cuts this off", so that you get e.g. recyclates such as scrap without any burden. Consequential is only if you are to model systems with a non-marginal, larger scale change. I hope this helps!