In calculations of spherically symmetric collapse to form black holes, trapping horizons make their first appearance either within the collapsing matter or where it joins on to a vacuum exterior. Ones moving outwards with respect to the matter have been proposed for replacing the global concept of an ``event horizon'' in the case of dynamical black holes. Using the Misner-Sharp formalism, we have studied the causal nature of both ingoing and outgoing horizons during collapse of idealised stellar models, with two complementary approaches focusing, respectively, on null-congruence expansion and on the horizon velocity measured with respect to the matter. The stellar models are simplified, but have a physically-motivated pressure, unlike the so-called ``dust'' models, and we find that this plays an important role in general. Comparison between the two complementary approaches leads to some new insights including giving pointers towards possible changes due to quantum effects if energy conditions are violated.