  We show that, after the change of variables $q=e^{iu}$, refined floor
diagrams for $\mathbb{P}^2$ and Hirzebruch surfaces compute generating series
of higher genus relative Gromov-Witten invariants with insertion of a lambda
class. The proof uses an inductive application of the degeneration formula in
relative Gromov-Witten theory and an explicit result in relative Gromov-Witten
theory of $\mathbb{P}^1$. Combining this result with the similar looking
refined tropical correspondence theorem for log Gromov-Witten invariants, we
obtain some non-trivial relation between relative and log Gromov-Witten
invariants for $\mathbb{P}^2$ and Hirzebruch surfaces. We also prove that the
Block-G\"ottsche invariants of $\mathbb{F}_0$ and $\mathbb{F}_2$ are related by
the Abramovich-Bertram formula.
