Both seems to mean "to add". What are the differences? Any other words that could be used alongside these?
For one, 加える is more formal than 足す。 足す can also mean to add, as in adding numbers / mathematics. The really small difference is that 足す is generally used when adding to an already existing quantity, while 加える is more used when adding something new. Examples:
Both mean to add sugar to coffee, but the former would be used in a scenario when I am creating a latte or some other sweet coffee beverage. The latter means to add sugar, as in the coffee already has sugar, but it's still too bitter.