catalog_category_product_index is an index table. In Magento, index tables are generated from the content of other tables.
The product id in this table refers to products in the table
entity_id, most likely the same).
If you reindex with the command you mention, and no changes have been made to any products or categories since the last reindex, the product ids will be exactly the same.
- All products that have not been deleted since the last reindex will have the same product id in this table.
- If you have added products since the last reindex, this table will have more rows, with new product ids.
- If you have deleted products since the last reindex, this table will have less rows - these product ids will be missing.
- If you have deleted and re-created products since the last reindex, you will not find the product ids of the deleted products anymore, but new product ids instead.
In most cases, I would say, in the day-to-day business, the product ids will remain the same.