Visit and Visitor based segments can and should give you very different results. A visit based segment will only include the visit where the defined action takes place, where a visitor based segment will include every single visit for a visitor where the defined action takes place.(both before, during, and after the order)
So if I am a visitor who orders on my 3rd visit, a segment that shows visits with orders will only show the interactions in my 3rd visit, but a segment that shows visitors with orders will show all of my visits (both before, during, and after the order).
Similarly, a segment that excludes visits with orders would only exclude my 3rd visit, but my 1st and 2nd visit would still be visible. Where a segment that excludes visitors with orders would exclude all of my visits (both before, during, and after the order).
We would need to see the entire report and the exact segment definitions used in order to give a full explanation. There's something that doesn't add up here, and I think it's because there are missing components to the segment/report that we can't see.