Cornets are nearly identical to trumpets*, including the total length of the tubing (were you to unwind it and form into a straight line), so they play in the same key. I have long collected cornets because the variations in how makers “wrapped” the tubing made for endless numbers of interesting designs, unlike trumpets, which are all more or less the same.
Pocket Cornets (also called Miniatures, Parlor Models, and Tourist Models) are nothing more than cornets which have had their tubing wrapped in an exceptionally compact design, resulting in an instrument 7 or 8 inches in length, yet playing in the same key and tonal range as their full-sized counterparts.
According to period literature, Pocket Cornets were primarily intended for travel purposes, as novelty instruments, or for use by small children. Here is a link to one of the earliest known pockets, actually a pocket cornopean, circa 1850.
Pocket Trumpets are nearly the same, except that they have slightly larger receivers to accept the larger trumpet mouthpiece. In fact, aside from the mouthpiece receiver, some of the pocket trumpets I’ve examined are really pocket cornets with respect to their design “wrap.”
Nearly all vintage Pocket Cornets utilized removable leadpipe shanks or bits. Most often, the cornet would be delivered with two shanks -- a short one for playing in “Bb,” and a longer one which convert the cornet to “A.” With shank & mouthpiece inserted, the cornet would be longer than the previously indicated 7 or 8 inches -- perhaps as long as 10 or 11 inches with a short “Bb” shank (12 or 13” with the longer “A” shank).
These vintage instruments were often made to play in so-called “high pitch” (HP): +/- A=452Hz. Later instruments are “low pitch” (LP): A=440Hz. Some cornets came with a second tuning slide to make this conversion. I have fabricated LP slides for several of my instruments.
While I cannot absolutely determine the point at which removable shanks were rendered obsolete, the AMATI and Alexander pocket cornets of the 1960’s were surely among the last to have this feature (I do not indclude the “decorative” copies being made in India). Only recently have I been able to document one of the earliest pocket trumpets, a Calicchio, as having been made in the late 1940’s.
*Historically, cornets are said to be “conical bore” instruments, in that the diameter of the tubing gradually increases from start to end; while trumpets are “cylindrical bore,” meaning that the tubing maintains diameter until the final flare of the bell. In actual practice, however, it turns out that cornets and trumpets are nearly identical in the percentage of conical bore. (source: measurements taken by Robb Stewart)