Does constant-depth, polynomial-size family of circuits mean that each circuit in the family has a depth that is bounded by a constant or that all the circuits in the family have the same depth (and so the depth of the family is constant)?
And if we say that the size of a circuit is bounded by a polynomial, do we mean that its size can be a polynomial or that it has to be less than that?
Constant depth means there is a constant $M$ such that every circuit $C_n$ in the circuit family $\mathcal F$ has a depth that is $\leq M$.
To say the family of polynomial-size circuits, is saying each circuit $C_n$ with $k$ input gates, has $poly(k)$ gates, in total.
One can identify each circuit as a DAG (directed acyclic graph), where each gate in the circuit is a vertex in the graph.