How to export only content, strictly core content like articles, pages, users, taxonomy ect?
There are several ways to achieve this


Use migrate module
Use Node Export Module
Use Feed Module
Or you can use web services to achieve this. For example expose data in services and import those data back in the other drupal site. (Very easy approach)
You need to check the database structure a bit and write a custom php script to take data from one table and insert it into another.