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 the 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 apge title, and one returns an old page title.
Why is this happening? Is it something on my side or Google's?