The extent to which this period prior to the festival becomes an active part of the observance is emphasized by a query posed by R. Shlomo Kluger (Resp. HaElef Likha Shlomo, #384). He discusses a situation where two questioners simultaneously approach the Rabbi on Purim: one with a question concerning Purim, and one with a Pesach question. Which question should be answered first? He leaves the question unresolved; while one might think Purim issues would be prioritized, as it is Purim at the moment, the fact that it is also thirty days before Pesach (see Pri Chadash 421:1) makes Pesach a current reality as well.
Many other Rishonim, however, understand there to be an active obligation to expound the day from thirty days before. This leaves the question, then, as to how to reconcile the two passages. In the understanding of some commentaries (see Bach and Gra to O.C. 601) the fundamental rule is expounding on the day itself, but that obligation expands to begin a month earlier.
R. Chaim Aharon Turtzin (Kuntres Chanukah U’Megilah, Megilah #3) suggests that the two concepts are actually fundamentally different. The obligation that begins a month prior is for the purpose of knowing the relevant laws of the festival, and is structured as such. (See Mishnah Berurah for a discussion of the possibility that the period is shortened for less complicated festivals).The obligation on the festival itself, by contrast, is more of a homiletic nature, to publicize and underscore the theme of the day. Similarly, as R. Yitzchak Sorotzkin observes (Gevurot Yitzchak, Purim, 25) the Kr’iat HaTorah on the festival becomes a fulfillment of that second aspect.