To count votes would be to count all votes.
To tally votes is to count them into their respective statistical columns.
I have 10 cookies of 2 different flavours. The count of cookies is 10.
The tally would be to sort the 10 cookies into their respective flavours.
i.e. after sorting the cokkies the tally was 4 choc-chip cookies and 6 double-choc cookies.
This is why a vote count and a vote tally are two different things.