acid base - What is the difference between these equations for the Contact process?

Some webpages describe the contact process as this (I left out $\ce{SO2}$, $\ce{SO3}$ production):

$\ce{SO3 + H2SO4 -> H2S2O7}$

After this, it is controllable to add water to the oleum therefore making liquid sulfuric acid. However, some other sites describe this:

$\ce{SO3 + H2O -> H2SO4}$

I am confused about what really happens in the absorption tower. I've read about the wet acid, but it states that adding water causes gaseous $\ce{H2SO4}$ to form, which is condensed.

EDIT: In the absorption tower, trioxide sulfur enters as gas, and sulfuric acid comes down as liquid. As a result the liquid comes out as oleum (first eq.). The other contact process states different: the liquid entering is 98% sulfuric acid, and 2% water, this water reacts with the sulfur trioxide (this little water avoids the heat problem), giving strengthened sulfuric acid (let's say 99.5% sulfuric acid, and 0.5% water). Still confused.