Adam Savage did a lovely section on this in Every Tools a Hammer.
To answer you’re question though, different glues work differently, but at the base mechanics for most glues, we have something that is either “wet” and has a lot of long spindly things, think jelly fish. When these “dry” those long spindly things tighten up and grab things.
This certainly applies to pva, wood glue, and super glue.
This also sort of applies to epoxies, just instead of drying, one of the ingredients makes the long bits shrink down and grab stuff.
For why some are “absolutely horrible” theres different needs for glues, for your example, it would be terrible to use construction adhesive on craft paper, school glue sticks are nice because after they dry, the glue remains flexible. Meanwhile, super glue has basically no flexibility upon curing, and epoxies can be hit or miss.
Also note, some glues spindly bits simply don’t grab onto certain materials, or they don’t really grab onto each other.
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