Surahs: Surahs were divided by Allah (subhanahu wa ta’ala) himself. But, the bulk of the names were neither given by Allah (subhanahu wa ta’ala) nor Prophet Muhammad (sallallahu alaihi wasallam). For the names that Prophet Muhammad (sallallahu alaihi wasallam) gave, he gave multiple names. Since names are just labels, they were given by Sahaba. Hence till date there are different surah names in Quran in different parts of the world. Eg: Surah Tabarak is same as Surah Mulk

Ayats: Every ayat (verse) is an indication that this book is from Allah (subhanahu wa ta’ala). Allah (subhanahu wa ta’ala) also divided the Quran into Ayats. But since the Quran was revealed verbally and not written by Prophet Muhammad (sallallahu alaihi wasallam) – the Quran was written by the Sahaba later – the number of ayats for some surahs are different between different Qurans. Note, it doesn’t mean an ayat is missing. The Quran has been preserved. It’s just an ayat that may have been merged.