die Party
party
A private or public social event for celebrating, usually with music, dancing, food, and drinks.
Am Samstagabend gehen wir auf eine Geburtstagsparty.
On Saturday evening, we're going to a birthday party.

party
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party
A private or public social event for celebrating, usually with music, dancing, food, and drinks.
Am Samstagabend gehen wir auf eine Geburtstagsparty.
On Saturday evening, we're going to a birthday party.

For the word 'Party' (party), the preposition 'auf' is crucial. You use 'auf eine Party gehen' (to go to a party, accusative) for movement and 'auf einer Party sein' (to be at a party, dative) for location.
Gehst du heute Abend auch auf die Party von Julia?
Are you going to Julia's party tonight too?
To express that you are hosting a party, use the verbs 'eine Party geben' (to give/host a party) or 'eine Party machen' (to have a party). Colloquially, you also often hear 'eine Party schmeißen' (to throw a party).
Meine Nachbarn geben am Wochenende eine laute Party.
My neighbors are having a loud party this weekend.
'Party' (party) is often combined with the occasion for the celebration to form a new word. Typical examples are 'Geburtstagsparty' (birthday party), 'Abschiedsparty' (farewell party), or 'Überraschungsparty' (surprise party).
Die Kollegen organisieren eine Abschiedsparty für sie.
The colleagues are organizing a farewell party for her.
event
'Party' and 'Veranstaltung' can both mean an organized gathering with several people. However, 'Party' fits especially when people are celebrating, often with music, food, drinks, and a relaxed atmosphere. 'Veranstaltung' is more general and more neutral. It can also include a concert, a lecture, a sporting event, or a conference. Learners may confuse the words because a party is also a type of event. But not every event is a party. When fun and celebration are the focus, 'Party' sounds more natural. When speaking generally or more officially about a planned event, 'Veranstaltung' fits better.

Am Samstag macht Lena eine Party mit Musik und vielen Freunden.
On Saturday, Lena is having a party with music and lots of friends.
Im Sportverein beginnt heute eine Veranstaltung für neue Mitglieder.
An event for new members starts today at the sports club.