The people with which the Dragonborn completed the quest depends on the faction they are aligned with but the quest for the most part is identical for both sides. The quest is completed in both the Imperial Legion and Stormcloak paths of the Civil War questline in which both factions are attempting to recover the crown.
Follow Legate Rikke (If the Dragonborn joined the Stormcloaks: 'Galmar').Meet Legate Rikke (If the Dragonborn joined the Stormcloaks: 'Galmar') outside of Korvanjund.Talk to Legate Rikke (If the Dragonborn joined the Stormcloaks: 'Galmar').(If the Dragonborn joined the Stormcloaks: 'Help the Stormcloaks drive the Empire out of Skyrim.') I should talk to Legate Rikke (If the Dragonborn joined the Stormcloaks: 'Galmar Stone-Fist') to get my first assignment.
I've decided to join the Imperial Legion in its fight to preserve the Empire.
