Learn Polish: Mamy tę samą wersję wydarzeń. - We have the exact same version of events.

The verb mamy (we have) requires a direct object in the Accusative case. The feminine noun wersja becomes wersję. The phrase ta sama (the same) must match this. The feminine Accusative of the pronoun ta is tę. The adjective sama takes the standard Accusative ending -ą to become samą. While you might hear native speakers mistakenly say tą samą here, tę samą is the strictly correct form!

Doesn't sama usually mean 'alone' or 'by herself'?

Yes! When used on its own, sama means 'alone' (for a feminine subject). However, when paired directly with a demonstrative pronoun like ta (this), the phrase ta sama completely changes its meaning to 'the exact same'.

Why do the two nouns in this sentence have different endings (wersję vs wydarzeń)? Are they in different cases?

Exactly. They are in two different cases doing two different jobs. Wersję is in the Accusative case because it is the direct object of the verb mamy (we have a version). Wydarzeń is in the Genitive case because it means 'of events' and describes the version. It is very common to have an Accusative object immediately followed by a Genitive descriptor.

How did the neuter noun wydarzenie (event) become ?