Cohomology classes $H^{1,1}(M, \mathbb{C})$ on Kaehler manifold

Question

I am confused about this and I would appreciate your help.

Suppose you have a Kaehler manifold $(M, \omega).$ Let $\omega_1, \omega_2$ be two $(1,1)$ forms belonging to different cohomology classes in $H^{1,1}(M, \mathbb{C})$. Is it possible that they both belong to the same class in $H^2(M, \mathbb{C})$?

How are $H^2(M, \mathbb{C})$ and $H^{1,1}(M, \mathbb{C})$ related to each other?

Thank you.