Another Catholic here--and yes, it is 40 days from Ash Wednesday until Easter, with Sundays not counted. Sundays are not counted because *every* Sunday is a feast day in honor of the Resurrection (call it a mini-Easter, if you will).
Why does the date of Easter move around? Well, the simple answer is that the date of Easter was originally tied to the date of Passover (just like it happened in the narratives of the Gospels). The Jewish calendar is a lunar calendar, and "slips" relative to the solar calendar. You see the same thing happen with the dates of Jewish holy days such as Rosh Hashanah, Yom Kippur, Passover (Pesach), etc. It's just that, for the most part, the number of people following the Christian holy days (whether they are Christian or not) is far larger than the number of people following Jewish holy days (how many non-Jewish people really pay attention to when Yom Kippur falls?), so the movement of Easter is noticed more often than the movement of Passover.
Early in the Christian era, it was decided to always observe Easter on a Sunday (as Passover can start on any day of the week, and while the date of Easter was strictly tied to the date of Passover, that meant that Easter could fall on a day of the week other than Sunday) due to that "every Sunday is a mini-Easter" line of thought (putting it simply--I mean, there is a *lot* of writing on the subject if you really want to get into it).
I'm not sure at which point it was, but at some point further down the course of history, it became less important in the Western Church to tie Easter and Passover together, so that the rule is that Easter will fall on the Sunday following the full moon after the vernal equinox. So, if the full moon happened to fall on the date just before the vernal equinox, you'd have to wait for the next full moon (throwing Easter well into April). The earliest possible date for Easter therefore is March 23 and the latest possible date is April 25.
The Orthodox consider it necessary for Easter to follow the start of Passover, therefore their observation of Easter may fall on a different date than those who follow the Catholic dating (which, interestingly enough, includes Protestants).