Summary
Currently, there are 2 distinct collection modules:
- The New Collections Module
- The legacy CMS Module
This difference is detailed here: https://help.vtex.com/en/tracks/catalogo-101--5AF0XfnjfWeopIFBgs3LIQ/3moFonW33dgOYDrU21Z1X0
The legacy module has two distict data clusters, the collection (A) and the group name (B)

However, the new collections module nly displaus the collection name, not its GroupName:

The Intelligent Search result are based on the Group Name, which is why, on cases that updates are done only on the new UI, the results are not reflected on the front end and the search queries.
Simulation
1 - create a collection using either UI 2 - update the collection on the new application only, making no changes to the legacy. 3 - check the search results and see it'll not be updated.
Workaround
Manually update the GroupName on the legacy UI and click "Save Group" to reindex the collection.