The origin of the use of the word "canning" is somewhat in dispute. In the USA it likely results from our tendency to shorten words. The process involves a "pressure canner" as distinguished from a water bath process. People just shortened the term to canning which is often used now for both processes.
Another possibility historically is that the process was invented in the late 18th century by Nicolas Appert in France in response to a call by Napoleon Bonaparte for a system of supplying French troops with preserved food that could both be easily transported overseas and actually eaten. Appert’s invention used fragile glass bottles, however, and it was only with the substitution of durable tin cans by Peter Durand of England that the process really took off and led to a worldwide revolution in preserving food. The containers were called cannisters which shortened became cans.
The problem with the original tin cans was that the joints were soldered and lead poisoning could result. I beleive originally in the USA domestic canning with cans was a thing.
Domestic bottling is a small scale thing in the UK normally reserved for fruit.
Just remembered a couple of things, with bottling we didn't tighten the lid fully until they came out of the pressure cooker, then as they cooled the seal was made by the higher pressure outside pushing the glass down onto the rubber seal. Then you always checked before storage and before use that the seal was good. Tin cans are completely sealed before going through the cooker and the contents are at atmospheric pressure. Originally tin cans were done in the same way as glass bottles, these days, a small vent was left in the lid then after cooking while still hot this was sealed with solder..