What each of these is for
The diagnostic answers one question quickly: is anything technical stopping search engines from reading and indexing your site properly? That is the first thing worth ruling out when traffic or rankings fall, because no amount of content or link building matters while a site is blocked from being indexed.
The checklist is the slower, manual version. It covers the same ground plus the things no automated scan can judge, and it is written so you can work through it yourself.
Neither replaces someone looking at your specific situation. If the scan comes back clean and you still are not growing, the cause is usually competitive or structural, and that is what the SEO Audit and 90-day roadmap is for.