The Mabinogion is a loose collection of eleven or twelve prose stories originally written in mediaeval Welsh (Middle Welsh), often published together in translation.
The name however is a mistake, going back about 700 years.

The Mabinogi is the central topic of this site, a set of four closely linked tales.

So there is the Mabinogi (4 linked tales) and The Mabinogion (11 varied tales).
The Mabinogi is always included in the larger group The Mabinogion.

The Mabinogi's sections (its Branches) end by saying 'And so ends this mabinogi.'
One of them, the ending of the First Branch, says it as 'mabynnogion' modernised as 'mabinogion'. This is thought to be a simple mistake by the mediaeval writer.

From at least the 18thC onwards scholars often assumed this was a plural word because -on or -ion is a Welsh plural ending.\\So 'mabinogion' was used as a title for this loose collection of eleven tales when published together.

It was not finally established that the word mabinogion was a mistake until the first half of the 20thC. However after 200 years of using it, the name had became established as a title. Many found it convenient to continue to use it to refer to the larger collection of eleven tales.

It can help to remember that the longer word mabinogion is the larger collection of eleven tales. This always includes the smaller mabinogi of four tales, which is a smaller word. The smaller mabinogi is also found published on its own.

~ An example of the correct wording is 'A llyna ual y teruyna y geing honn o'r Mabinyogi','And so ends this mabinogi'.¹⁾
~ The old error mabynnogyon is mediaeval in origin. It only appears once at the end of the First Branch, nowhere else. The line which shows the error is Ac uelly y teruyna y geing honn or mabynnogyon.²⁾
~ These statements about the end point of 'this mabinogi' are often referred to as a 'colophons' i.e. a publisher's note explaining something about the work.
~ One theory is that the scribe who was copying the manuscript was tired, so made a slip in spelling. Just above the line the word dyledogyon, 'noblemen', appears, which possibly confused a tired copyist with its ending. This was then faithfully recopied onwards in later manuscripts.
~ The pioneering first publication of a Mabinogi story in print by William Owen Pughe in 1795, used 'mabinogion' in its title.³⁾ Pughe then used 'mabinogi' in titles for other stories he published later.
~ The famous 19thC Charlotte Guest is often thought to have pioneered the title The Mabinogion in 1838, but in fact she was following existing Welsh tradition.
~ Guest's publications included a Taliesin tale, making her collection a total of 12 stories. All other publications of The Mabinogion collection omit this, because the Taliesin tale survives in a different manuscript. The standard group is therefore eleven tales.
~ Patrick Ford in 1977 made a strong move to separate the 'Native Tales' from the later Anglo-Norman ones. His translation is therefore titled The Mabinogi and Other Medieval Welsh Tales. Ford does include Taliesin, on the grounds it is a native tale, but not the three Romances, or the two Dream tales.
~ Sioned Davies in 2007/ 2008 returned to using the title The Mabinogion for the eleven tales, because she felt it was an established convenience.

John K. Bollard gives an excellent and detailed analysis of this issue about the name and the manuscript error. He explains there is little to connect the tales of The Mabinogion together as they had different authors, were created at different times, and in different styles.
John K. Bollard, ‘What Is The Mabinogi? What Is “The Mabinogion”?’, (2007).
<https://sites.google.com/site/themabinogi/mabinogiandmabinogion>