Method of canning without pressure canner

Pressure cookers and pressure canners are the same thing; with the canners being larger, and often having a pressure dial. Both can reach the same pressures and therefore temperatures if designed and manufactured correctly

The pressure canners dial gauge is more accurate for adjusting for food types and altitude, as you can get exact numbers not just 10 psi and 15 psi as with typical weight regulated pressure cookers. But for low acid foods you need 15 psi anyway

Pressure preserving is done because of the higher temperatures reached. This saves time and energy, and some food react better to a short 250°F (120°C) cook that an long 210°F (100°C) cook

Pressure preserving high acid food is worth doing as long as the food does not deteriorate quicker due to the high temperature (some soft fruits will)

For preserving low acid foods you need a known good pressure cooker that can reach 15 psi (103 Pa) and therefore 250°F (120°C)

With a commercially published recipe that has been acid level tested, you will have a published time that will be safe. For a home-made recipe you have to take the worst case scenario for the acid level of the main content, and cook for that. Your local government health department will most likely publish tables for this that you should be using. Remember to use altitude adjustments for timings too

Just relying on adding a teaspoon of vinegar or lemon juice per jar is not a safe and scientific method for raising the acid level, though many people do it, and have not come to any trouble with it?

You pressure cooker should come with a manual that confirms what it can or cannot do. Download a new copy if this has been lost

Also see What kinds of pressure cookers are there, and what are they good for?

The trusted recipes you get from, e.g., a university extension are tested to make sure that they actually heat through entirely and for long enough to destroy bacterial spores, in particular botulism (but also a few more less deadly ones).

In water bath canning, you're using acidity (primarily) to make sure botulism can not grow from the spores, which are not destroyed by boiling water canning. The inside of the jar isn't actually sterile.

In pressure canning, you're actually destroying the spores. So you can can things where the bacteria could otherwise grow—because the inside of the jar is sterile.

Destroying the spores requires reaching a particular temperature for a long enough duration. If you don't do that, once the food cools down, the spores will germinate. A very bad outcome.

The key thing is that (as always) the outside of whatever you're canning heats first. The heat then transfers in towards the center. But the rate of heat transfer can vary greatly depending on what it is.

If heat transfers slowly, you have to pressure cook longer. If heat transfers quickly, you don't have to cook as long. Generally, you'd like to process for as short a time as possible, to preserve texture and flavor.

When developing a safe canning recipe, multiple batches are prepared and each is canned with special equipment that allows measuring the temperature at various points inside the jar, during the pressure cooking. They time how long it takes for all the points to reach safety, and of course repeat this multiple times. That's ultimately where the processing time comes from.