I made some significant On Page SEO changes to a site recently to optimize for a particular key word. My site was on page 5 of the Google SERP.

I noticed that today, 12 hrs later, my site has been updated in Googles "cache", and the changes I made are reflected when I use the cache: keyword to look up the site. Although, my position in the SERP has not changed.

My questions is:
Is the google cache and their search index one in the same?

For instance, if they've updated the cache does that mean they've re-ordered me in their search as well based on the most recent factors?

I noticed that position in the SERPs has not changed for my target keyword, even though I've supposedly made significant "on page" optimizations for that keyword. I was suprised that my rank hadn't budged.

Thank you!