If I were to want to create a PHP function that does the same thing as the Export tab in phpMyAdmin, how could I do it? I don\'t know if there is a MySQL function that does
You can check the phpMyAdmin source code (an advantage of open-source software). Check the export.php script and the supporting functions in the libraries/export/sql.php script file.
In summary, what phpMyAdmin does is:
I've written similar code for my own apps (for backup purposes, when the GPL license of phpMyAdmin doesn't allow me to use it), however I use DESCRIBE to get column definitions. I think they rather parse the SHOW CREATE TABLE output because contains more information than DESCRIBE output.
This way to generate SQL sentences requires a bit of care to handle the escaping but it allows for some flexibility, as you can convert types, filter or sanitize data, etc. It is also a lot slower than using a tool like mysqldump and you should take care of not consuming all available memory (write soon, write often, don't keep everything in memory).
If you will implement a migration process (from server to server) maybe it would be easier to do it with some shell scripting and calling mysqldump directly, unless you will do everything with PHP.