Learn English – Difference between “a” and “the”

Well, a simple dictionary lookup tells us a lot. Let's have a look at oxford online.

Basically, form as a noun is _always countable, except in the following cases:

-1.2 [MASS NOUN] Style, design, and arrangement in an artistic work as distinct from its content:
these videos are a triumph of form over content

-2. A particular way in which a thing exists or appears:
essays in book form
energy in the form of light

-4. [MASS NOUN] The customary or correct method or procedure:
an excessive concern for legal form and precedent

-7. [MASS NOUN] The state of a sports player or team with regard to their current standard of play:
they are one of the best teams around on current form

-7.2 A person’s mood and state of health:
she seemed to be on good form

-7.3 British INFORMAL A criminal record:
they both had form

The only use that is confusing, because one example uses form as a mass noun, the other as a countable noun, is meaning 2. Of course, that is also the way form is used in your text.

In the first instance in your text, the sentence follow exactly the example given: in book form versus in electronic form. The question is where the article comes from in the second instance.

In the second instance of form in your text, the reference is not to electronic form in a general sense, but it is about a specific shape (form) in which the information is to be presented: a shape that can be processed by computers. The simple transformation into electronic form as mentioned earlier is no longer adequate to describe it, we need now to specify a specific electronic form. We can conclude there are other forms which may be electronic, but can not be processed by a computer.

So when we describe the way in which a thing appears or exists, we only use form as a mass noun when we refer to the general concept described by that way of existence:

Literature usually appears in book form.

But when we talk about a specific instance or type of that way of existence, we use it as a countable noun:

Paper encyclopaedia were not exactly a portable book form.

Note that in the construction in the form of , form is always countable!

I would say they are both correct, and have the same meaning in this context. The difference between "a" and "any" is hard to explain, but you can think of it like this:

Is there a house? Yes. Are there any houses? Yes, there are 3.

If there is a house, there is one house. Even if there are multiple houses, one house is included in that.

If there are any houses, there are some houses there. There may or may not be more than one.