What is the difference between these equations for the Contact process?
In principle, your sources are correct and not contradictory.

In order to avoid the formation of problematic sulfuric acid mist, sufur trioxide is not directly absorbed into water. Instead, it is absorbed in sulfuric acid of 98 %–99 % concentration, which approximately corresponds to an azeotrope where the partial pressures of sufur trioxide, sulfuric acid, and water are relatively low.

Sulfuric acid reacts with the absorbed sulfur trioxide to form disulfuric acid:

$$\ce{H2SO4 + SO3 &lt;=&gt; H2S2O7}$$

The disulfuric acid can be converted to sulfuric acid by reaction with added water:

$$\ce{H2S2O7 + H2O &lt;=&gt; 2 H2SO4}$$

Thus, the overall net reaction is as follows:

$$\begin{align}
\ce{H2SO4 + SO3 \;&amp;&lt;=&gt; H2S2O7}\\
\ce{H2S2O7 + H2O \;&amp;&lt;=&gt; 2 H2SO4}\\
\hline\ce{SO3 + H2O \;&amp;&lt;=&gt; H2SO4}
\end{align}$$