Jam and jelly are made from fruit, fruit juice, sugar, and pectin. The main factor preserving these foods is the acidity of the fruit. The acidity will prevent the growth of the bacteria that causes botulism. Caution is advised when making jam/jelly from borderline acid fruit such as banana, Asian pear, melon, and watermelon - these recipes should be research-based and include added acid such as lemon juice or citric acid. Canning jams and jellies in boiling water will kill other microorganisms and seal the jars creating a vacuum. Canned jams and jellies are shelf stable.
NCHFP Resources - Types of jam/jelly, general info, extracting juice for jelly, remaking jams or jellies, includes many recipes plus low sugar versions.