Manually Add Twitter Account in Contacts.app in Mountain Lion
What you're looking at in your first screenshot are the Instant Message fields. The second screenshot shows the so called Profile field. The Profile field seems to be the same as the Twitter field. So, if you want to add a Twitter handle to any contact go to Card > Add Field > Twitter (or Profile). This works even if there's no Twitter match for that contact.



Alternatively, you can display the Twitter field by default by editing the card Template.