Think of the 'shape' of the top of a world's groundwater as being an alternate surface of the planet. Everywhere it's above 'ground level' there's water - river, lake, ocean. Everywhere it's below the dirt/rock surface, it's an underwater reservoir or flow. The two surfaces are related - if the dirtlevel dips, the water that's 'exposed' is fluid instead of contained between rock particles, and it puddles. That modifies the shape of surrounding groundwater to match at the new shoreline.

The wetlands you mention are just where the two surfaces almost match. Yup, one would assume in the days before people succeeded in draining or filling in wetlands to make use of the land, there would've been more. Wetlands can be source of streamflow, or destination, or a intermediate pause. Figure they constitute lakes that are almost filled in (which is sometimes how they form) or flattish land that has acquired an overabundance of water (can you say "flood"? I thought so :-) ).

Too bad marshes are so tricky to depict!