3. The quality, clarity or sharpness of speech.
2. Mode of utterance or pronunciation, especially as regards fullness and distinctness or articulation; as, to speak with a clear or impressive enunciation.
The main usage of "articulation" that I have heard is the phrase: "He/she is very articulate." This means that the person is able to express themselves very well in clear, concise language.
Enunciation is close to pronunciation. I was once told to make sure that I "enunciate my words very well." (i.e. speak clearly).
Looking at the definition of enunciate on Wiktionary, it seems it can be a synonym of pronounce or articulate.
3. To articulate, pronounce.
So it appears that there is only very subtle differences in these words. They are not ones that most people will use on a day-to-day basis, and I struggle to find a setting I would use these words, except in a discussion such as this one. Most people I know would simply say "speak clearly" or "that person seems to know what they're talking about!" and similar phrases.
People are waiting to help.
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