Creating custom versions of parent theme theme for a child theme

I read the WordPress Codex about the utility of child themes in preserving customizations in the event that the parent theme updates. So I made a child theme for the site and started using it.

I need to make several customizations to the theme, which are scattered across many of the PHP files that make up the parent theme. Do I need to make corresponding copies of each of those PHP files, with the entire content (modified to a small extent)?

I have a doubt about this approach. If I make so many corresponding files, the updates to the parent which include potential bug fixes (other than my customizations) do not appear in the child theme. Isn’t that the same as making all changes to the parent theme and disabling the updates?

Thanks and regards,
Dhruv