(covers information from several alternate timelines)
A medical ship was a starship whose primary function was to be used for medical purposes, because of this, they were typically not well armed with weapons or other defensive systems. This could include vessels described as hospital ships, medical transports, or medical frigates.
Various species and cultures had ships of this nature.
The Federation had several ship designated for medical purposes. One of these, the medical frigate classified USS Hiawatha, was lost in 2256, during the Federation-Klingon War. Its wreckage was accidently discovered by USS Discovery and some of Hiawatha's survivors were subsequently rescued. (DIS: "Brother")
In the anti-time future, the USS Pasteur was a medical ship, operated by Starfleet Medical, as indicated by its emblems on the primary hull and their prominent presence on the bridge. In that same future, the Klingon Empire conquered the Romulan Star Empire and grew hostile towards the Federation.
In 2395, there was a Terrellian plague outbreak on Romulus. Federation medical ships had permission from the Klingons for crossing the border, so they could deliver medical supplies to the planet. Still, Pasteur was destroyed by the Klingons, as it had wandered into their space without permission, though its crew was rescued by the timely arrived USS Enterprise-D. (TNG: "All Good Things...")
One subject discussed at a conference on Romulus during the Dominion War in 2375 was a proposal to transfer twenty-five Federation hospital ships to the Romulans. (DS9: "Inter Arma Enim Silent Leges")
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