A distinction without a difference is an informal fallacy where an author or speaker attempts to describe a distinction between two things where no discernible difference exists. [1] It is particularly used when a word or phrase has connotations associated with it that one party to an argument prefers to avoid.
For example, a person might say "I did not lie; I merely stretched the truth a little bit." [2]
In the following conversation:
Sergio's fallacy is thinking that being taught by someone is different than taking a lesson.