part two other modern dictionaries are in agreement with collins and a google search. Impudent sometimes used by some speakers as interchangeable with impertinent. impertinent = same as impudent but impertinent also = "not pertinent" not related impertinent not showing proper respect; rude. "an impertinent question" rude, insolent, impolite, unmannerly, ill-mannered, bad-mannered, uncivil, discourteous FORMAL not pertinent to a particular matter; irrelevant. "talk of ‘rhetoric’ and ‘strategy’ is impertinent to this process" Impertinent originally meant just what it sounds like, "not pertinent, irrelevant," but it also came to mean "inappropriate, out of place" and therefore "intrusive, presumptuous; behaving without proper respect; insolent." It still carries a condescending air, so it's best used of or to a child being snippy to a grownup: "Don't be impertinent!" The stress is on the second syllable: im-PERT-inent.

They are close synonyms. If I had to find a distinction, "impertinent" behaviour probably relates only to words, while "impudent" behaviour could relate to words, actions or both.

A modern or current English dictionary will give the same definition to both words. But etymologically (historically) the word impudent meant not ashamed unashamed. and the word impertinent meant "not related to" "not to the point" according to some sources impudent is considered obsolete, for the word immodest and impertinent is considered obsolete for the word "not pertinent" not related. However you have to be aware that there are still some speakers who use these definitions in their speech and writing. Therefore the context will sometimes be important to know which definition is being used. Miriam webster dictionary says this impertinent : not restrained within due or proper bounds "especially of propriety or good taste" no reference to being obsolete. Impudent obsolete : lacking modesty 2 : marked by contemptuous or cocky boldness or disregard of others : INSOLENT The Cambridge dictionary says this Impudent rude and not showing respect, especially towards someone who is older or in a more important position: an impudent remark/child impertinent it gives the same definition and example. rude and not showing respect, especially towards someone who is older or in a more important position: an impudent remark/child Oxford dictionary says this. Impudent Not showing due respect for another person; impertinent. ‘he could have strangled this impudent upstart’ impertinent Not showing proper respect; rude. ‘an impertinent question’ the oxford dictionary gives the subtle etymological historical difference that was once used. The collins dictionary says this 1. the same as the other modern dictionaries. 2. an obsolete word for immodest