They do, but I also know my old boss has used Grado SR80e's as his in-office cans for a desk in an open floorplan office for years. It's not going to be more audible to your coworkers than light whispering.
There's definitely a difference, because hearing aids aren't designed for music fidelity, they amplify speech ranges primarily. But, as far as safety? What possible mechanism do you think there is whereby hearing aids (which are speakers inserted into the ear) would be less dangerous than... any other kind of ear-level speaker? If you look at a wiring diagram for a Tinnitus Retraining Therapy ear-level noise generator, or a hearing aid, it is... a speaker attached to speaker wires.
Let's turn this around. If hearing aids and ear level noise generators were somehow magically safer than equivalent noises out of other kinds of headphones, why isn't anyone selling headphones based on that technology?
Some people have unscientific and unreasonable views about headphones. I'll be the first to admit that putting speakers of any kind right next to your ear probably isn't a great idea if you're not being very diligent about it. The thing that grinds my gears is that people want to draw some kind of distinction between TRT devices, hearing aids, and other speakers, and... it just doesn't exist? Like, there's no data, we've had this argument in one direction for years, and ... no data has ever emerged. On the one hand we have thousands of peer reviewed papers indicating that sound waves are sound waves and function in specific ways; on the other we have... people who are... really scared of headphones for some reason, and seem to have an agenda about it?
Some people in this forum think their tinnitus is affected by the phases of the moon, the color yellow, toothpaste, having used hairdye once years ago, and someone two streets over getting a dog. (I am not making any of these up, they are real things I read here).
It's not a very compelling source of exciting information, especially when that information flies in the face of rock solid scientific data about how sound works and is processed by the human hearing apparatus.
You have yet to materialize any peer reviewed data showing specific risks related to headphones; if this is a concern, why is there no clinical data, given the millions of clinical tinnitus cases which now exist in large data sets? It seems very strange to me that something so significant and scary would be completely absent from the relevant research.
And to be very clear -- I do think lots of people get tinnitus from headphone use. I just don't think headphone use poses any specific audiological risks that other equivalent noise doesn't, because believing that is basically like believing in faeries. (I will also start believing in faeries if suddenly they are popping up all over and being documented in Nature).