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any / no ~ (not) a/an

Although your paired example sentences are both possible, we don't usually use any with singular countable nouns in English. For the singular, we would probably use a different formulation. Compare:

• There aren't any trees along this road.
• There isn't a single tree along this road.

There is a slight difference of emphasis here, which is also implicit in your own paired example. In the first sentence, we are thinking of more than one tree and in the second just one.

So, to summarise, the difference in use is that we employ an indefinite article an/a or not a/not an with singular countable nouns and any/no with plural countable nouns and with uncountable nouns. Uncountable nouns, meaning 'an amount of', normally have no plural. They are thus used with singular verbs, BUT with any/no rather than a/an/not a/not an. Compare the following:

• Would you like an egg for breakfast? (One egg = singular countable noun)
• No thanks. I don't want any eggs today. (More than one
  egg = plural countable noun)
• I'm making scrambled egg for Joe. Won't you have any scrambled egg? (Scrambled egg = uncountable noun)

some ~ any/no

Note the principal difference in usage between some and any. We tend to use any in questions and with negatives, some in affirmative sentences:

• Is there any information (uncountable) about any survivors (countable) from the plane crash?
• No, I'm sorry there's no information available yet. (OR: … there isn't any…BUT …no…preferred because it has stronger emphasis)
• As soon as we have some, we'll let you know.

any = it doesn't matter who or which

There is one instance of usage where any is quite common with singular countable nouns and that is when it means 'it doesn't matter who or which'. In speech, the word any itself carries strong stress. Study the following:

• Any good dictionary will give you examples of use as well as definitions of words.
• Any British daily newspaper will give you some information on the weather in the world's capital cities.
• Any child under the age of ten can enter the egg-and-spoon race.
• Ask any dentist and he will tell you that you should go for a check-up at least once a year.

no one/nobody/someone/somebody/anyone/anybody something/anything/nothing

Note that there is no significant difference in use between -one and -body, except perhaps that -one is more commonly used. Note also that no one is the only one that is written as two separate words.

I think the clue as to why they are all used with singular verbs lies with -one, meaning one person, or one thing or not one thing or not one person. Compare the following:

• There's someone at the door who wants to interview you.
• There are some people at the door who want to interview you.
• I'm sorry, I'm busy right now. Isn't there anyone else who can do it? What about Fred?
• Some relationships last for a long time but nothing is for ever.