I'm thinking they should sound the same in both peninsular and Latin American Spanish. If that's true then why the spelling change?
Pronunciation would be the same. However it is a question of orthographic rules. Before an -e or an -i, for a [z] sound we will always write it with a -c. We don't have words with -ze or -zi, they will all be written ce or ci.
Some examples are: cine, cena, hacer, encima, Francisco, cisne, acelerar..
Hope this helps
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