I am totally new in Drupal, and I am using Drupal 7. I was asked to move data between two sites that don't even have the same structure, and have different fields.
Can anything bei done with a tool like Drush, or with MySQL?
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You could possibly use views to output the data you want into a csv file (with views data export module) and then import the data into the destination site using Feeds module. This technique has worked well for me on a number of occasions.
Additionally, you could try the Features module but this is quite complicated and may be difficult to get your head around initially.