The reason why the coordinates don't fit exactly is that we determined the coordinates in the year 2000, which is the year the International Astronomical Union works with. Because of the rotation of the Earth, the stars are "moving" each second and the coordinates change consequently. That's why scientists always work with the coordinates of a fixed date.
You can also try it by yourself. If you change the date and time in Stellarium you'll see that the coordinates always change a little :)