I am using Sharepoint 2013 Foundation version.

I have set up 2 environments (say environment A and environment B) with the same Window baseline and Sharepoint server farm setup. The similar set of documents have been uploaded to both environments. With input of exactly the same search string at the search field and enter button pressed, the sequences of entries shown on search result page are different in these 2 environments.

In particular, there is a document 'Monthly Newsletter.pdf' uploaded in both environments. When I type 'Monthly Newsletter' in search field and press enter, this document appears as the first entry in the search result in environment A, but this same document appears as the 8th entry in the search result in environment B. 

May I know the reason? Thanks a lot for advice!

There are a lot of factors that go into computing the "relevance" of any one document. One factor is "closeness". So one question would be how identical are the two environments? Same number of site collections? Are the documents at the same depth? (sites -> subsites -> libraries -> folders)  Are the libraries of the same type, using the same content types and the same metadata>  In both cases are you searching from the same site and are the documents at the same depth?  

Ranking is also impacted by past searches. The more people who have clicked through to the document, the higher it will be ranked in the future.

If the two environments are identical, and are only being used for testing, Reset the Indexes and do a new Full Crawl and then test.

Thanks a lot for your information!

May I know what is closeness and how it affects search result? Are the search result which is 'closer' will be ranked first and displayed first in the search result list?

Here is supplementary information to your questions.

So one question would be how identical are the two environments? Same number of site collections? > Yes, each environment has one site collection only and each site collection contains the same number of sites. But how is this number affects search result?

Are the documents at the same depth? (sites -> subsites -> libraries -> folders)  > Yes, the number of documents and the folder structure are exactly the same.

Are the libraries of the same type, using the same content types and the same metadata>  Yes, the same.

In both cases are you searching from the same site and are the documents at the same depth?  Yes, the same.

Ranking is also impacted by past searches. The more people who have clicked through to the document, the higher it will be ranked in the future. > This is the difference I can think of. I know this feature is available in Standard version and Enterprise version. May I know whether this feature is also provided in Foundation version?

Thank you!