You will only ever have logs of requests made to your own pages. If someone requests an external page, it shows up in their logs not yours ;)
A quick explanation of how server logs work - sorry if this is more technical than you need. Your logs will be made up of lots of lines like this:
22.214.171.124 - - [17/Apr/2003:17:34:51 +0100] "GET /internalpage.htm HTTP/1.1" 200 3297 "http: //www.referrer.com/link-to-your-page.html" "Mozilla/4.0 (compatible; MSIE 6.0; Windows 98)"
What this basically says is that the IP (126.96.36.199) on 17 April, requested internalpage.htm (succesfully hence the 200 status code) which is 3297 bytes in size, and they were referred by www.referrer.com/link-to-your-page.html. The last line is the web browser or user agent that requested the file. Every request for a new page, image etc. writes a new line to the log file. This makes up the number of 'hits' on your site.
Logs can be a little confusing at first, so sticky me if you are really struggling with this. You can always use other methods to compile statistics on your site that don't use logs at all.
My suspicion is that whatever hostway are using for the statistics is not doing much more than aggregate numbers from the log file, hence using the terminology normally used to talk about raw logs (requests, hits) rather than the sort of info that is useful in reporting on site traffic (unique visitors, page views).