The Suffrage badge is awarded to a user who casts 30 votes on questions and/or answers in a single day.
The Vox Populi badge is awarded to a user who casts 40 votes, the daily limit. It is possible that a user won't be able to use 40 votes in a day as is explained here.
Do we really need both badges? Don't they reward effectively the same behaviour? If you haven't already received the Suffrage badge, won't it be awarded to you on the same day you get the Vox Populi badge?
The Suffrage badge is much older than the Vox Populi badge, when the Suffrage badge was introduced the absolute vote limit was 30 votes.
The Vox Populi badge was introduced at the same time as the increased vote limit was implemented.
The badges are somewhat redundant, but introducing two badges in this situation is still better than e.g. changing the definition of the old badge.
The motivation is described in links from the answer you linked to. The limitations on Vox Populi described at the link make it harder to get the badge if you vote primarily on answers, so it (imperfectly) rewards not only voting a lot, but voting a lot and including a lot of votes on questions.
In addition to Mad Scientist's point that it was probably just easier not to change the older badge, keeping the Suffrage badge leaves a badge that is easier to obtain, and it rewards many for voting a lot, even if they will never vote enough (or include enough question votes) to get Vox Populi. In practice, there are many Suffrage recipients who have never received Vox Populi. There are probably many who have both but who received them on different days.
