Let $G$ be a split semi-simple simply connected group over a global field $F$ and let $\omega$ be a top-degree differential form on $G$ without zeroes (defined over $F$). It is well known that $\omega$ defines a measure on the adele group $G(\mathbb A)$. The Tamagawa number formula states (if I understand correctly) that

1) If $F$ is a number field then the volume of $G(\mathbb A)/G(F)$ is 1

2) If $F$ is a functional field isomorphic to $\mathbb F_q(X)$ where $X$ is a projective curve over $\mathbb F_q$ then the above volume is equal to $q^{(g-1)\dim G}$ where $g$ is the genus of $X$.

My questions are the following:

a) Do I understand the statements correctly?

b) What is the reason why 1) and 2) look somewhat differently? Can one formulate the statement in a uniform way for all global fields?

Edit: In fact my understanding was wrong. In 1) one needs to multiply by the volume of $(\mathbb A/F)^{\dim G}$ which is equal exactly to $q^{(g-1)\dim G}$ in the functional case. I was confused by the case $F=\mathbb Q$ where the above factor is 1.