(covers information from several alternate timelines)
The medical tricorder was a specialized version of the standard Starfleet tricorder. It was equipped with sensors and analysis software tailored for medical diagnostic purposes. They were usually the first tool a Starfleet doctor utilized when assessing a patient's condition. Medical tricorders could function aboard ship in sickbay as well as on away missions. (TOS: "The Man Trap")
Medical tricorders used throughout the years have been essentially similar in design to that of the standard tricorder, with the same available features and interface. The major difference is the addition of a deployable hand scanner. (TOS: "The Man Trap"; TNG: "When The Bough Breaks")
Although very accurate on the living, it is taught in the first year of Starfleet Medical School that medical tricorders are not as accurate on the dead. (DS9: "The Passenger") Additionally, a medical tricorder scan was no substitute for a complete autopsy. (TNG: "Man of the People", "Suspicions")
A medical tricorder could, in certain instances, provide a recommended course of treatment for an individual in hostile terrain. Captain Lisa Cusak followed the advice of her medical tricorder when stranded on a Class L planet to give herself fifteen CCs of tri-ox every four hours to compensate for the excess carbon dioxide in the atmosphere. (DS9: "The Sound of Her Voice")
Medical tricorders were in use aboard the Enterprise NX-01 during the mid-22nd century. In 2153, Doctor Phlox noted that Sim had disassembled Phlox's medical tricorder, when commenting on his aptitude for engineering. (ENT: "Similitude")
TR-560 Tricorder VI
The medical tricorder in use by 2364 was essentially similar in design to that of the standard TR-560, a flip-open device with the same available features and interface. The major difference was the addition of a deployable hand scanner tucked into a module at the very top of the tricorder. (TNG: "Encounter at Farpoint", "The Naked Now") The scanner could provide detailed scans of an entire individual, or give focus to a single area. (TNG: "When The Bough Breaks")
This version of the tricorder was mostly supplanted by the TR-580 Tricorder VII in late 2366, although at least one unit was used aboard the USS Enterprise during the autopsy of Lieutenant Joshua Kelly in early 2369. (TNG: "Realm of Fear")
TR-580 Tricorder VII
By late 2366 Starfleet R&D introduced this iteration of the tricorder was very similar in design to the previous version but had a slightly altered color scheme and interface font. (TNG: "Transfigurations") It was not necessary to use the scanner for the TR-580 to function. The scanner could be separated from the tricorder, either to feed data to another source, or not be attached to the tricorder at all. (DS9: "Babel"; VOY: "Time and Again") The medical tricorder was also designed to work closely with the surgical support frames attached to biobeds. (TNG: "Identity Crisis")
The medical sensor unit was equipped with additional sensor ports. In conjunction with a neural pad, a medical TR-580 could be used to link the nervous system of a healthy individual to that of an injured individual in order to stabilize the injured for transport. Doctor Beverly Crusher used a tricorder to link Geordi La Forge to stabilize the patient known as John Doe. (TNG: "Transfigurations")
The tricorder could be used to record audio. Dr. Crusher used a tricorder to record mysterious voices she heard in her quarters while the Enterprise was trapped in a temporal causality loop in 2368. (TNG: "Cause and Effect")
This version of the medical tricorder was equipped with holographic imaging diodes. When Captain Jean-Luc Picard completed a computer program left behind by the ancient humanoids, the program reconfigured the tricorder to display a holographic message. (TNG: "The Chase")
They could be configured to remotely open doors and briefly disrupt a force field. Dr. Crusher and Captain Picard used a medical tricorder for these functions when escaping a Kes holding cell in early 2370. (TNG: "Attached")
TR-590 Tricorder X
Introduced along with the Mark X standard tricorder, a medical tricorder variant was in use aboard Federation starships as early as 2372.
Generally identical to the standard tricorder, the medical featured a detachable hand scanner (as in previous models) that fit into the back of the unit. The indicator lights on the top of the unit varied in color from red to yellow to blue. (Star Trek: First Contact; VOY: "Favorite Son", "Prey"; DS9: "Soldiers of the Empire"
In 2374, Seven of Nine described a medical tricorder she imagined in the following manner: "Duritanium casing. Seven point six centimeters by nine point eight centimeters by three point two centimeters. Alphanumeric display" (VOY: "Retrospect")
Introduced as late as 2379, yet another iteration of Starfleet tricorder departed from the distinct, flip-open style preceding it.
Distinguished by a slim, PADD-like appearance, the tricorder in use aboard such Starfleet vessels as the Enterprise-E in the late 2370s featured a large touchscreen interface. Silver in color, it was trimmed with black pads at the bottom and sides, with several buttons at the top. These buttons could be covered by a small hinged door, lined with indicator lights. (Star Trek Nemesis)
In 2258 of the alternate reality, the medical tricorder consisted of a scanning rod and handheld feedback monitor. (Star Trek) The following year, the scanner had been redesigned into a white oval-shape reminiscent of the previous monitor, and could be stored inside a normal tricorder. (Star Trek Into Darkness)
An extension of the Mark X model, this tricorder featured the familiar hinged cover design, but contained more touch control surfaces in place of toggle switches. It featured a small handheld antenna scanner. (VOY: "Endgame")
Gates McFadden, who played Dr. Beverly Crusher, requested a standard set of operating guidelines for props on Star Trek: The Next Generation. In response, illustrator Rick Sternbach developed a tricorder user guide, which was later incorporated into the Star Trek: The Next Generation Technical Manual (page 120).
In 1997, Playmates Toys produced a version of the TR-580 as part of their toy line. Several action figures throughout the run of the line were packed with miniature versions of medical tricorders as accessories.