There are a number of slightly different definitions in current use for the quartiles that are used in making boxplots.  Different quartiles, of course, can mean a different IQR, and that in turn can lead to different decisions about what is or is not nominated as an outlier.  Boxplots based on different definitions can look very different.  Large differences are most common with small data sets -- just the kind used for textbook examples.  The differences are not important for most real data.