In this lecture series, Stalnaker uses both verbs 'instantiate' and 'exemplify'. Now, I gather those two verbs have the same meaning. But, I also think that if the two verbs were equivalent, Stalnaker would rather choose one of them and stick to that verb.
This leads me to think that perhaps there is a difference, although the difference may be due to grammar only. (NB: I'm not a native speaker.)
I'm hoping that somebody here is familiar with either 1) Stalnaker's choice of words, or 2) a normal distinction between these verbs, in particular in (modal) logic or modal metaphysics. (And I hope that nobody will ask me to provide a transcript of relevant parts of the talks.)