This is a hypothetical example of an actual problem. I hope it's clear.
When I search Google for dogs I can see my website homepage
http://dogs123.com.au with the title "Dogs a mans best friend!".
If I search for dogs australia I see my website homepage
http://dogs123.com.au with an old page title "Dogs blah blah". Clicking through on this result gives the up to date, current page with the proper title.
i.e. for two different searches, returning the same result, one returns the correct page title, and one returns an old page title.
Why is this happening? Is it something on my side or Google's?