What's the difference between an -ing noun and a real noun

"developing" is not a noun. It's the form of a verb called the gerund, and it has a dual nature, -one of a verb and one of a substantive.

Its verbal nature is shown by a) its ability to take a direct and an indirect object. b) the fact that it can have a subject (I was proud of him being my son) c) is ability to appear in different tenses (he boasted of his having killed her)

Its substantival nature is shown by a) its ability to be the object of a preposition (by doing so)
b) the fact that it can take a plural ending (such going-ons) c) it can take an attributive adjective (his dangerous driving) d) its ability to take a definite or an indefinite article (a hanging was once a public amusement) The active form of a gerund is often used in a passive sense (your hair wants cutting, the garden needs weeding)

In parallel cases a noun ending in e.g. -ment would normally imply the result of an action, the product of an action while the corresponding gerund would refer to the action itself. Take for instance "extension" vs. "extent" or "export" vs. "exportation.

A gerund would normally have in it the verbal nature which the corresponding noun need/does not have. Compare "The king's arrival was met with much enthusiasm" vs. "We are quite tired of his usual arriving very late".

In the case of "developing" one might compare "The development of AIDS in Africa has proved to be one of the biggest tragedies in the Third World" vs "The new president aims at developing the country's poor-relief system".

It's true that you can sometimes generate a noun by adding -ing, like with "an understanding". It's not a universal rule, but in general, you can generate a noun that refers to the process of the verb — "a developing" sounds odd to me, but other examples, like "a ripening" (as in we can observe the ripening of the fruit) work for me.

But my main point is that even if you can generate an -ing noun from a verb, there's no reason to assume it would mean the same thing as a noun ending with -ment generated from the same verb. To respond directly to your first sentence, it's not that some verbs have a corresponding noun, but rather that many verbs have many corresponding nouns. If they always meant the same thing, we wouldn't need different suffixes.

You cannot use any word anywhere you feel like, while writing in English. That is the sophistication of English language. There are certain terms to describe certain moods.
The noun form of verbs by adding "-ing" are called gerunds. These should be used at the appropriate situations.

For example, you cannot say, Swim is his hobby. You have to say, Swimming is his hobby.

Whereas you can definitely say, I am going for a swim. Here you cannot say, I am going for a swimming.

Similarly, in your sentence, They thought that Tom would bring a big development for this small town is the correct one.

Now if you ask, When do I use gerunds and not the "normal noun" form? Well, that comes with practice.

It's OK to use developing as a noun (for example, developing is one of the stages of the photographic process), and the second sentence here is grammatical.

The reason it sounds strange, to this native speaker at least, is partly because the whole concept is a little fuzzy†, but mostly because we have a perfectly good and common alternative to developing: development. In cases where there is no alternative, the sentence sounds fine:

They thought that Tom would bring a big restructuring for this small town.

† Does development mean the general improvement and growth of the town, or does it refer to a single major development such as a shopping mall. If it is the latter, then developing is not possible.

I think you have got it wrong. Development is the noun form as in "That's a big development". But you cannot say that's a big developing. Developing is the gerund form of the verb develop, which can be used as an adjective. "Developing nations should form a committee..."

That said, developing is a noun but not the one you think.

Developing is a 1994 short film directed by Marya Cohn, about the relationship between a girl and her single mother, who has breast cancer. The film stars Natalie Portman as Nina.