I'm seeing inconsisntecies in table data after exporting from one server and importing to another, why is this?
From the symptoms, it seems that you are using InnoDB engine for your tables. If so, it is normal not to have accurate number of rows shown by clients (Like HeidiSQL or PHPMyAdmin). 

It is also worth it to mention that SHOW TABLE STATUS LIKE 'table_name' does not provide accurate row count for InnoDB tables. 

InnoDB estimates the number of rows in the table. If you want the exact count, you should run SELECT COUNT(*), as you just did.

MyISAM, on the other hand, has the information of its number of rows saved and 'always' up to date.

In regards to physical file size, there are many factors that leads to tables that have same date to have different file size on disks. Some are related to the operating system itself, and the file system used; some are related to the configs of MySQL; and some are related to the fragmentation of the data when doing deletes and updates. In short, this difference is very normal.