Geometric Brownian Motoin versus Square root proces

Question

Lets say random variable S(t) is changing according to a Geometric Brownian motion $$dS(t)=aS(t)dt+bS(t)dW(t)$$ where $W(t)$ is a standard wiener process. It is widely known that $S(T)-S(0)$ is distributed log normally with mean $(a-\frac{b^2}{2})T$ and variance $b^2T$. I would like to know if any such result exist in the case $S(t)$ is changing according to a "square root process". $$dS(t)=aS(t)dt+b\sqrt{S(t)}dW(t)$$. My attempt: Let $G=log(S)$. Applying ito's lemma one can see that $$dlogS(t)=(a-\frac{b^2}{2S})dt+\frac{b}{\sqrt{S}}dW(t)$$ Here the drift term is bigger than in the case of GBM. This tells me that possibly, the expected value of $G$ is higher in the case of square root process than GBM. But I have not been able to find any reliable resources, or go beyond this on my own.