die Urne
urn
A vessel in which the ashes of a deceased person are kept after cremation.
Die Urne wurde im Familiengrab beigesetzt.
The urn was buried in the family grave.

urn / ballot box
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urn
A vessel in which the ashes of a deceased person are kept after cremation.
Die Urne wurde im Familiengrab beigesetzt.
The urn was buried in the family grave.

The context makes clear which 'Urne' (urn/ballot box) is meant. Words like 'Wahl' (election) or 'Stimme' (vote) point to the ballot box. Terms like 'Asche' (ashes), 'Beisetzung' (burial), or 'Friedhof' (cemetery) refer to a funeral context. 'Ausgrabung' (excavation) or 'antike' (ancient) indicate the archaeological meaning.
Die Wahlbeteiligung war hoch, die Urnen waren voll.
Voter turnout was high; the ballot boxes were full.
In connection with a burial, the verbs 'beisetzen' (to bury/inter) and 'aufbewahren' (to keep/store) are typical. People also speak of an 'Urnenbestattung' (urn burial) or an 'Urnengrab' (urn grave).
Immer mehr Menschen entscheiden sich für eine Urnenbestattung.
More and more people are choosing an urn burial.
In a political context, there are fixed expressions such as 'zur Urne gehen' (to go to the polls) or 'an die Urnen treten' (to go to the polls), both of which mean 'wählen gehen' (to go vote).
Am Sonntag sind die Bürger aufgerufen, an die Urnen zu treten.
On Sunday, citizens are called upon to go to the polls.
vase
'die Urne' and 'die Vase' are both containers, but they are used in very different situations. A 'Vase' is usually in the home and is meant for flowers. An 'Urne' can be a vessel for the ashes of a deceased person, a ballot box for voting slips, or a historical vessel. The words can be confused because both can look like containers. In everyday use, however: flowers go in a vase, ashes or ballots go in an urn.

Nach der Feuerbestattung wurde die Urne auf dem Friedhof beigesetzt.
After the cremation, the urn was buried in the cemetery.
Auf dem Tisch steht eine blaue Vase mit frischen Tulpen.
There is a blue vase with fresh tulips on the table.