John,
A wet well is the large, usually round chamber that holds the long shafts of the vertical turbine pumps at the pump house/pump station. It connects to the irrigation lake allowing the pumps to suck water in for pumping.
As to water tanks, they are making a comeback. The theory is that lakes lose a lot of water to evaporation, and a tank doesn't so its a water conservation measure. Here in TX, and most of the south, evaporation is about 0.2-0.25 or more per day. If you have a two acre lake, that is about 10,000 Gallons a day, maybe 3 million gallons a year. It was never considered a big deal, although we never sized lakes bigger than we needed for about 7 days storage (just in case water supply was turned off) but these days, they are looking for every way possible to save water.
Obviously, capacity is an issue, but it sounds like you have a relatively small course irrigation need if the old tank worked. If you rebuilt with a new, probably some dug in and some above ground, you would be very trendy and environmentally conscious, and it might not cost a lot more than digging out your lake for more capacity.