To a large extent 'no' means 'zero' .. a quantity and 'an' (or a) means "one".
In that sense, you could not have both 0 and 1 plates at the same time. (that is why you cannot have "There is no an apple on the table."
If an definite plural was used (apples) "an" would not be used either.
NOT - is a different matter entirely - as BillJ points out, not works as an adverb altering inverting 'is' in terms of existense
So, basically your two cases are more different than you might think.
To help illustrate, lets look at 'plates'.
- "There are plates on the table."
- "There are not plates on the table"
Answer the question "do plates exist on the table?"
- "There are 8 plates on the table"
- "There are no plates on the table"
Answer the question "How many plates are on the table"
Now.. of course having a zero quantity is synonymous with 'nonexistent'
I would also note two curious side points that are probably part of the mental confusion:
The double negative of "There are not no plates on the table" is awkward at best which we might flip in our mind to conclude that 'no' isn't really referring to quantity
Also the inversion of "an" in its "one" sense with a "not" gets confused:
not one" is as often used idiomatically for an indefinite amount amount of nothing - in a round about way it refers to "none of the possible numbers of plates are there" ... so often so if there were two plates on the table and someone answered "there is not one plate" on the table, it would mean something different from "not 8 plates" on the table.