How are you copying the photos to the external hard drive? Are you dragging the "Photos Library" in the User>Pictures folder over to the external? The library is a single document that contains all the photos. Or are you dragging mass photos from within the application, i.e. while you have the Photos application open? Or another way?
For what purpose do you use the external HD? Just for a backup copy of all your photos? Do you take the external to someone else's computer to show them photos? Or something else?
For backup purposes, of course the photos should not be edited on the external...else they won't be an exact copy should you need to restore in the event of a crashed computer. To view or search for photos on the external, you should copy the "Photos Library" to the external HD. Then any computer with the Photos application should be able to open up that library. You can also try to copy the actual Photos application onto the external (I've never tried that). If that works, then any Mac that can run Photos will be able to view the pics.
If you are connecting the external HD to a PC or a much older Mac...well, they won't run the Photos program. Then, I suppose you'll have to use one of the other suggestions and copy the individual photos en mass (i.e. not the "Library"). I believe the Photos program is the only application that can view the Photos Library.
Or maybe you're just copying a bunch of photos, but not the whole library, onto the external. And not for backup purposes. Then I would refer to the other posts.
Sorry for the lengthy post. Just trying to cover everything.