What does the second website look like? There are some add-ons or services that may redirect to a new page that looks something like search results if a missing file is detected. If you regularly get to that kind of page, check for a link near the upper right or at the bottom which says anything like "About this page", "Why am i seeing this" or "Opt out". That may lead to more information about what is going on. You also could post the address of the unwanted page and let a support volunteer take a look at a it.

Where were you going, and where did you end up?