"A contraction is a word made by shortening and combining two words."
And wikipedia says:
"Contraction is also distinguished from clipping, where beginnings and endings are omitted."
You've managed to find and obscure reference somewhere that says somebody, somewhere, uses some other word nobody here has ever heard of to divide what we all understand by 'contraction' into two categories.
If you had been saying "that is not a contraction - it's a clipping" then you may have a case. You have not been doing that.
You've found this so-called explanation after the fact ... And, as we shall see, you stuffed up this one too.
You found a reference in gcflearnfree.com? Well who the hell are they. Never hear of it. That means nothing.
Then you found a quote somewhere in Wiki. I notice you don't say where.
So what does Wiki really say? ... in articles that have some relevance to us here.
This is from the article: https://en.wikipedia.org/wiki/Contraction_(grammar)
This is its first line. This is contraction means when used as a grammar term:
A contraction is a shortened version of the written and spoken forms of a word, syllable, or word group, created by omission of internal letters and sounds.
Then there's the Oxford Dictionary ...
3 [countable] (linguistics) a short form of a word
'He's' may be a contraction of 'he is' or 'he has'.
Note #1 - a shortened form a "a word" - not a group of words into one word.
Note #2 - The Oxford Dictionary does not mention any meaning for 'clipping' as any kind of shortening of word(s).
Then from dictionary.com ...
a shortened form of a word or group of words, with the omitted letters often replaced in written English by an apostrophe, as e'er for ever, isn't for is not, dep't for department.
Note - the example of e'er for ever
Then from the British English definition (copied from the Collins Dictionary and quoted within the dictionary.com entry) ...
a shortening of a word or group of words, often marked in written English by an apostrophe: I've come for I have come
Note - a word or group of words
You don't even your pathetic excuse of a rationalisation for what you've been saying right.
There is no explanation for what you want under 'clipping' in dictionary.com - you get redirected to "clipped form".
And what do you find under "clipped form"? ... something completely different!
The examples it gives for "clipped form" are:
deli from delicatessen
flu from influenza
doc for doctor
So when claimed " 'n' " should be called a clipping, not a contraction ...
Wrong #1 – Dictionaries call that "clipped form", not "clipping"
Wrong #2 - Clipped forms actually mean something quite different
Whatever it was you thought you found, it has no relevance to any of us here discussing writing. For us here, a 'contraction' always has, and still means, any shorting of one or more words into a single word, with apostrophes to denote omitted letters or words.