Google search is a massively different beast when it comes to searching, and you should in no way expect a site search to return similar results to Google.
Most notably, Google searches the entire page for the keywords you specified. That means it searches the question, the tags, the answers, the comments, and even the "related" column at the right. Google also doesn't always limit which pages it will look at, and will include things like tag wikis, question lists, and user profiles in the results. That potentially means you could end up with results which have absolutely nothing to do with Apigee, but simply have the word on the page somewhere.
Our site search, on the other hand, only searches on a per-post basis. When searching for a tag, it will return all questions with the tag and all answers under a question with the tag. Searching for the term will only returns specific posts which actually contain that term within them.
Past that, I'm actually not sure how it comes up with that 59,600 (mine shows 59,400) - that's just the number that Google Custom Search returns. The search itself only actually returns 100 results, so it's not possible to audit what all is being considered to be "on our network" in that search, and as mentioned by Normal Human Google even returns incorrect numbers when it's less than 100 results. An actual search on google.com for "site:stackoverflow.com apigee" returns only 3,200 results, which is a much more reasonable number to expect.