Is it like the trace is the result of movement and has to be in the chain with the head, while PRO is just a null duplication taken the position but with no phonetic realization?
Both PRO & Trace have no phonetic realisation, they belong to empty categories (null elements). I see that you took 'trace' in general, you have to specify which trace: (i) wh-tace or (ii) NP trace. Anyways, PRO is not a result of Movement like the trace, because in GB, PRO is taken to be a DS element (a pre-movement/transformation phase).
PRO has also a distinct theta role (even if it's coindexed). If an element is co-indexed with another element, it forms a chain. As you may know, empty categories are another requirement of grammar, i.e. Projection Pricniple, so traces and other empty categories guarantee the preservation of semantic information of either the: (i) moved elements (like NPs) or (ii) the in-situ elements like PRO.