Another AOL customer tries to access your site a few minutes later, but they never get to your site, the data is fed directly to them from AOL's cache, so your counter never records the visit. In addition the counter will only record visits to the page that it is actually on. It does not count visits to other web pages. So if the visitor never gets to the page with the counter on, the counter obviously never records them. Web sites are complex places.
Log files are a more accurate measure of visits, in that they record data for all pages.
However the same provisos about problems with counting remain . If you are sufficiently interested in more information on this subject, I have a more detailed analysis comparing the results of 4 different methods of counting on this page. Briefly a fairly typical hotel web site accumulated visits over time. A counter on the front page recorded around 2200 visits and different log analysis software recorded anywhere from 2350 to 2550 visits. While the log analysis for the whole site recorded a range of 5250 to 5850 visits.