Product and topic searches from one site appearing in the drop downs of another store/ different site

I have searched for music artists on itunes and sites like And frequently searching topics on various sites. To my surprise, some weeks later, when I was shopping at an unrelated site, the drop down when I clicked on their “search” for their products contained a 1/2 dozen subjects and music groups that had nothing to do with the site I was currently on. This has happened other times on at least one other site. I have tried going to settings/clear browserda ta, selected all time, and this did not delete the drop down topics. 2 questions: why is this happening and, how can I stop this from occurring in the future?