Vtyjkyuk

So I have a group of people. Each of them is 60% likely to vote on A and 40% likely to vote on B. What type of distribution does this create if I'm looking for amount of people that vote on A - the amount of people that vote on B? I'd say it would just be a difference of binomials, but they are dependent on each other so I'm not sure.

It's just a shifted, scaled Binomial. Essential, you want a weighted Binomial: $X_1,dots,X_n$ are i.i.d. Bernoulli random variables with parameter $3/5$, and you are looking for
$$
X = sum_k=1^n (2X_k-1) = 2sum_k=1^n X_k -n = 2Y-n
$$
where $Y$ is a Binomial with parameters $n$ and $3/5$.

Let
$$
I_n=begincases
1 & textif the ntext-th individual votes for A\
0 & textotherwise.
endcases
$$
Assuming voters do not influence each other, then $I_1,ldots,I_N$ are i.i.d. $operatornameBernoulli(0.6)$ random variables.
Let $V_A$ be the total number of voters for $A$ and $V_B$ be the total number of voters for $B$.
Then,
$$
V_A-V_B=left[I_1+cdots+I_Nright]-left[N-left(I_1+cdots+I_Nright)right]=2left(I_1+cdots+I_Nright)-N
$$
where $I_1+cdots+I_N$ is a binomially distributed $operatornameB(N,0.6)$ random variable.