The homology class associated to a hypersurface?

Question

Let $X$ be a compact complex manifold of dimension $n$ and $Z$ be a hypersurface. I want to know about its homology class $[Z]\in H_{2n-2}(X)$.

Some methods I know to define $[Z]$:

1. Find a line bundle $L$ which has a holomorphic section vanishing precisely on $[Z]$, and $c_1(L)\in H^2(X)$. Then its Poincare duality gives $[Z]\in H_{2n-2}(X)$. (This is equivalent to the definition of fundamental class. This is the part I can understand)
2. The image of $1\in H^0(Z)$ in the composition $$H^0(Z)\xrightarrow[\text{ isomorphism}]{\text{Thom}} H^2(X,X-Z) \to H^2(X)$$ defines a class in $H^2(X)$ and then its Poincare duality gives $[Z]\in H_{2n-2}(X)$.

My questions:

1. Both methods need to define the cohomology class first and use Poincare duality. Is there a direct way to define $[Z]\in H_{2n-2}(X)$?
2. Why the two definitions are compatible?