You should use function str_to_date() to convert your strings to actual DATE type. After that, you can use period_diff() to compute difference in months, but you have to convert your date using date_format() into format that is supported by period_diff (which is confusingly is NOT a date).
Final SQL is (SQLFiddle Demo):
SELECT period_diff(
date_format(str_to_date(`to`, '%M %Y'), '%Y%m'),
date_format(str_to_date(`from`, '%M %Y'), '%Y%m'))
FROM mytable
One note though: I don't quite understand where did you get 15 and 11 from. This query gives difference between from and to in months, and for your data it is 14 and 23 respectively. Just to demonstrate, I have also added current month as from and to, and it does indeed compute to 0 difference.