I’ve made some definitions more clear on Critical Successes and introducing the idea of Critical Failures more definitively to my games of Dungeons and Dragons 5e.
General Rule
A natural 20 will ALWAYS count as an automatic success on any d20 test, regardless of nature. However, this comes with downside of a natural 1 always being an automatic failure on any d20 test.
Criticals on Attack Rolls
While narrative liberties will be taken on skill checks and saving throws. Attack rolls will work differently. A critical success will allow you to roll your normal damage dice and add on a second dice roll. This includes all dice that are involved in the dice rolling, such as Sneak Attack, Divine Smite, etc. Should you roll maximum damage with any damage dice, you can roll again for additional damage. This rolling damage continues until you don’t roll maximum damage. However, a critical failure on an attack roll can have drastic consequences. There will be a fumble table rolled on by the DM which will determine if your attack just glances off and goes wide, or if your attack hits a friend…
Critical Failure of Spellcasting
Spellcasting can be a dangerous and confusing art, if completed wrong a spell could have dangerous consequences. There are several ways that Wild Magic can surge around the casting of a spell. One is the roll of a critical failure involved in the casting of a spell. When this occurs there is a chance of a Wild Magic Surge, which the DM will have you roll for.