Probably the switch from DWI to DUI occurred over time as confusion over terms just like above happened. Back in the days when some of us had to walk uphill both ways to school through 6' of snow there weren't insurance requirements. Didn't hit this area until the mid 80's as I recall. About the time manditory liability hit the books, the changover from DWI to DUI in referring to driving while under the influence happened.
Now that I'm thinking back on it, there was a distinction between DWI and DUI then. DWI was for being over the limit, DUI was for being under the limit, but still driving erraticly. At this point I think it's switched to DUI being above the limit and Suspicion of DUI as Michael said for under. Do remember a case where one of my parent's coworkers got a DWI reduced to a DUI though back in the timeframe I was talking about.