Albert Einstein said:
If you can't explain it simply, you don't understand it well enough.
Using overly verbose language (both large and obscure terms, particularly when smaller ones are just as effective) doesn't imply intelligence, it actually usually implies
arrogance. Admittedly, this is partially due to the listener easily feeling somewhat inferior due to you going over their head; no one likes to feel lesser than another person, even when the speaker isn't trying to come across as such. Sometimes
trying to help people will also get a similar effect, because you can puncture their pride (even if it's there for a faulty region) by doing so. Simple people take what they can do very seriously, sometimes being a little too direct with your assistance can be more detrimental to both you and them.
And this where the above quote comes into play. The ability explain complex & abstract concepts in a way that your average or lay person can understand (usually involving the use of an analogy) shows that you
really understand the concept, you can accurately compare the idea to a seemingly unrelated idea to make it more accessible to all. It's elegant use of language... which does sound similar to "eloquence", but I don't think the phrases are directly related.
To tell the truth, using big words should be kept to a minimum in all but a few situations. If you're discussing the technical aspects of a subject with your fellow experts in a field, use of more specialized terminology (or jargon) helps because you need more precise language; and everyone present should be familar with that language. Even then, knowing when to put in the simple explanation is very useful. Another situation when one can use more verbose language is when you're deliberately trying to go over another's understanding, but that should be saved for when the listener has
earned your ire and really needs their arrogance quelled. This does run the risk of backfiring catastrophically, because they actually might be able to understand it; leaving you looking like the actual fool. The final situation is when using complex language is something of a joke, which may be followed up with the simple explanation just as well; the verbose explanation is the set up, the simple explanation is the punchline.
I've got to be careful myself about using complex terminology, because I can easily use them without considering the fact the people I'm talking to don't have any idea what I'm talking about. I've come across as arrogant when there was no intention to do so. To tell the truth, some of the courses I've taken (complimentary studies in sociology for example) have annoyed me for using overly complex language unnecessarily; they're attaching a longer term to a concept, almost as if they're trying to take ownership of the idea,
while a much more simple term already exists.
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In summation:
A "smart" person uses big words, because they think it makes them
look smart.
A smart person knows the big words, but uses the simpler ones because they
understand what those words really mean.