The Google reCaptcha is a 'one-size-fits-all-designs' widget that does not offer many styling possibilities. In this age of responsive designs, it is actually interesting to see that Google does not offer a good solution when it comes to reCaptchas.
The first version of the widget used to offer a 'raw' theme, which was fully skinnable. Version 2 is unfortunately not giving such option.
Custom reCaptcha plugin is trying to address the shortcomings of the Google reCaptcha widget. It is a complete solution for users of the Google widget, from the ones who are still using the now unsupported first version to the ones who want to use the next generation of the reCaptchas, the invisible one.