Argument to the stick is the English meaning of 'argumentum ad baculum'. In the word by word translation, the noun 'argumentum' means 'argument'. The preposition 'ad' means 'to'. The noun 'baculum' means 'stick'. Stick is not referring to a stick as in a twig or a branch, it is referring to an object like a club that is used to hit things, like the club that police carry around. They carry it around, because they use it to make people stop doing things like running away from them.

An argumentum ad verecundiam is an argument from authority, or an appeal to authority.

An argumentum ad passiones is an appeal or argument intended to convince the listeners by agitating the emotions.

An argumentum ad populum is a fallacious argument which concludes that a proposition is true because many people believe it.

An argumentum ad Lazarum is an appeal to poverty - a logical fallacy that a conclusion is correct because the speaker is poor.