When you need an index
A single sitemap may hold 50,000 URLs and 50 MB uncompressed. Beyond that — or when you want separate files for pages, posts, products and images — list the files in a <sitemapindex>. An index can list up to 50,000 sitemaps, and child files may be gzipped (.xml.gz).
An index cannot list another index, and its <loc> values must be absolute URLs. Put each child sitemap’s own last change date in <lastmod> so crawlers only re-fetch files that changed.
Questions
Can an index point to sitemaps on another domain?
Only if you have verified both hosts in Search Console, or the other host’s robots.txt references the sitemap. Same-host is simplest.
Do I submit the index or every sitemap?
Submitting the index is enough; Search Console then reports on each child.
Can I nest indexes?
No. A sitemap index may only list sitemap files, not other indexes.
The creator already split my sitemap — do I need this?
No. The creator writes the index automatically when it splits. Use this tool to combine sitemaps produced by different systems.