I thought I’d start a new topic with this since it appears not to be a permissions issue. I thought I had solved previous problem by attaching the problem drive to a different Mac, erasing, renaming, reformatting, and copying the files back to it. But no.
On my MacBook Air, the SSD external mounts correctly, as an external drive. And it mounts as external drive when attached directly to one of the iMac’s USB ports. If I attach it to my external OWC Thunderbolt dock, attached to iMac, it mounts as an INTERNAL drive. I have three other external drives attached to that same dock, also via USB, individually, not daisy-chained, and they all mount correctly as externals. They all are regular drives, not SSD. I can live with this, grumpily, but am fascinated. When attached to another OWC thunderbolt drive connected to the Air, it mounts correctly as external. Both Macs on latest High Sierra. What gives?