The best example I can provide at the moment would be to look at all the connotations of the word "love". We have romantic love ("I love my husband"), familial love ("I love my brother"), friendly love ("I love my best friend Nan"), preferential love ("I love pizza, but I don't love sushi"), spiritual love ("I love God"), and so forth. A trivial example of the Connotation Substitution Fallacy would be something like:
Ana: I love my friend Nan.
Troll: That is patently untrue. You do not love Nan because you have no intention of marrying her. You do not love Nan because you have never invited her to be present at the Mardoll Christmas gatherings. And you do not love Nan because you do not worship her as an ascended higher being.
The fallacy here is that the Troll has latched onto a word in the premise ("love") and has decided to ignore the contextual connotation (friendly love) and apply inappropriate-to-the-topic-at-hand connotations (romantic love, familial love, spiritual love). The key to diagnosing this fallacy is that it only works because English uses one word ("love") for multiple ideas -- if we replaced all the words with their connotative meanings, the argument would be nonsense. (Note: Total abuse of the Greek language coming up.)
Ana: I philia my friend Nan.
Troll: That is patently untrue. You do not eros Nan because you have no intention of marrying her. You do not storge Nan because you have never invited her to be present at the Mardoll Christmas gatherings. And you do not agape Nan because you do not worship her as an ascended higher being.
(Content Note: Rape Statistics) A less trivial use of the fallacy would be when a study defines a specific target group, like "stranger", and someone substitutes in a colloquial definition of that term when discussing the study.