What is the difference between ΔfH and H-H° in NIST–JANAF tables?
As a side note, &quot;JANAF&quot; stands for Joint Army–Navy–Air Force; these tables were designed to provide quick access to the thermodynamic data for rocket scientists.
Here, $Δ_\mathrm{f}H^\circ$ is the standard enthalpy of formation. The difference $H-H^\circ(T_\mathrm{r})$ is required to calculate the standard enthalphy of reaction $Δ_\mathrm{r}H^\circ$ if in the given temperature range a reaction takes place.
There is a thorough explanation in Silbey's Physical Chemistry [1, p. 62]:

The JANAF tables give standard enthalpies of formation at a series of temperatures, and so these values may be used directly to calculate enthalpies of reaction. [...] Some thermodynamic tables give values of $\bar{H}^\circ_T - \bar{H}^\circ_{298}$ to assist in the calculation of $Δ_\mathrm{r}H^\circ$ for a chemical reaction or phase transition:
$$\bar{H}^\circ_T - \bar{H}^\circ_{298} = \int_\pu{298 K}^T \bar{C}^\circ_P \mathrm{d}T$$
Depending on the table, $Δ_\mathrm{r}H^\circ$ for phase transitions in the intervening temperature range may be added to the right-hand side of the equation.

NIST-JANAF tables are given for a reference temperature $T_\mathrm{r}$ and a standard state pressure $p^\circ$. Unless stated otherwise, $T_\mathrm{r} = \pu{298.15 K}$ and $p^\circ = \pu{0.1 MPa}$ [2].
References

Silbey, R. J.; Alberty, R. A.; Bawendi, M. G. Physical Chemistry, 4th ed.; Wiley: Hoboken, NJ, 2005. ISBN 978-0-471-21504-2.
NIST-JANAF Thermochemical Tables, 4th ed.; Chase, M. W. J., Ed.; American Institute of Physics: Washington, DC : New York, 1998. ISBN 978-1-56396-831-0.