If there was no correlation whatsoever, then you'd expect 100% of people to vote "difference" for each dichotomy, and 0% to vote "same".
If everybody identified in both systems with three out of four dichotomies, you'd get on average 75% of people voting "same" for each dichotomy, while having no apparent 1:1 correlation between the two systems (i.e. people having the 'same' type in both).
The average for people voting "same" is about 77%...and this does not take into account people who voted for neither "difference" or "same" for a particular dichotomy.