A label for multiple equations

Yes, it is possible by using split environment, and the tags are:

\begin{equation}\label{General}
\begin{split}
A &\sim a,\\
B &\sim b,
\end{split}
\end{equation}

You can use an aligned environment nested within your equation:

\documentclass{article}
\usepackage{amsmath}

\begin{document}
\begin{equation}
    \begin{aligned}
        A &\sim a,\\
        B &\sim b,
    \end{aligned}
\end{equation}
\end{document}