Being informal (not formal) is when a person speaks, writes, or behaves in way that is not strictly polite, courteous or grammatically correct. People generally are informal around their family and friends or in text messages and e-mails, hence the word"in-formal".
Being impersonal (not personal) is when a person speaks, writes, or behaves in a way that is not personal, subjective or heartfelt. People generally behave this way around people they do not like or do not know very well, hence the word "im-personal"
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