Which make HCO3- to show two pH values at two scenarios?

According to the below two titrations,

Image Reference

If we consider the reactions, at the first reaction (in first figure after adding 1.0), there is $\ce{HCO3-, NaCl,}$ and $\ce{H2O}$ at the first equivalence point. At the second one (after adding 1.0), there is $\ce{HCO3-,}$ and $\ce{H2O, Cl-}$ at the first equivalence point. $\ce{HCO3-}$ only affect to the $\mathrm{pH}$ of the medium. But,

• According to the first figure, $\ce{HA- + H2O → H2A + OH-}$ it acts as a base
• According to the second figure, $\ce{HA– + H2O → A2– + H3O+}$ it acts as a acid

I am doubtful on why do $\ce{HCO3-}$ perform as two types at these different situations? Do anything in the medium manipulate $\ce{HCO3-}$ to work as a base or an acid? How to describe these two scenarios? Generally I can't see a theoretical method for describe it.

I searched this in so many resources, but I couldn't find a satisfied answer. So, I hope a theoretical answer, for this problem, not a mathematical description.