In Inferno the souls are what they did; in Purgatory they are ceasing to be it. That is the central difference, and it is why Inferno punishes and Purgatory heals, and why here, unlike there, one sings. The souls of the mountain know that their punishment has an end, and they want it.
The text shows the difference in scenes. Forese calls the punishment he suffers a consolation, because the will that leads him to the tree is the one that led Christ to say Eli. Statius, after more than five hundred years, feels his will free to climb, and the whole mountain trembles with praise. The mountain itself weighs heavily at the start and lightens with each step, and Virgil measures progress by this weight, not by distance.
The guide changes too. In Inferno Virgil knew the way; in Purgatory he has to ask, reason aloud and pray to the sun, and the poem makes this a lesson about the reach of reason. The company changes as well: instead of the damned, who repeat what they were, there are poets, princes and popes who speak of their own error from the distance of someone who now sees it. And the center changes: Inferno arranges the sins by kind, while Purgatory reduces them to a single root, love, and shows the will being straightened along the way.
That is why the cantica speaks most to the life of someone trying to change and not yet succeeding: it has relapse, haste, waiting and slow progress.