How do you determine the NIE equation of a buffer?
$\ce{HCHO_2 + H_2O &lt;=&gt; H_3O+ + CHO_2-}$ and $\ce{HCHO_2 + OH- &lt;=&gt; H_2O + CHO_2-}$ are both reactions that can happen.
If you added $\ce{HCl}$ (of high concentration), you added a strong acid, and there will be extra hydrogen ions. Therefore, it will drive your first reaction backwards due to the extra hydronium: $\ce{H_3O+ + CHO_2- &lt;=&gt; HCHO_2 + H_2O}$.
If you added $\ce{NaOH}$ (of high concentration), you added a strong base, and there will be extra hydroxide ions. Therefore, it will drive your second reaction forwards: $\ce{HCHO_2 + OH- &lt;=&gt; H_2O + CHO_2-}$.
Distilled water has no buffer added to it, and it is not a buffer itself because of extremely low concentrations of $\ce{H_3O+}$ and $\ce{OH-}$. Tap water might have buffers in it. Lakewater have buffers to prevent sudden changes in pH. For example, it might have limestone at the bottom of the lake, which serves as a buffer against strong acids. As an example, when acid rain falls, it brings with it sulfuric acid, and the buffers prevent the pH from dramatically decreasing, by the equation $\ce{H2SO4 + CaCO3 =&gt; CaSO4 + H2O + CO2}$. With the buffers, the fish living in the lake will not be affected by the sudden changes in pH, otherwise, they might stress or even die (but that's a question for Biology SE).