Ability patches give hidden abilities. So, say I wanted Long Reach on decidueye, I would use that. Ability capsules give regular abilities, but switch them. So, say I have a lanturn, which has water absorb and illuminate as its 2 main abilities. I currently have illuminate, but to get water absorb I would use the ability capsules.
Source:experience(and getting many incorrect abilities lol)
(And now an edit cause no one should trust me and I don't trust myself)
If used from the Bag, it changes a Pokémon's Ability from one of its standard Abilities to its Hidden Ability. It cannot be used to change a Pokémon's Ability from its Hidden Ability to one of its standard Abilities.
If used from the Bag, it changes a Pokémon's Ability from one of its standard Abilities to its other standard Ability. It can only be used outside of battle. It is consumed after use.
Source 2 I guess