Learn English – The possessive case of multiple nouns

As noted in comments, it's generally (unofficially) discouraged to use "women" or "woman" as an adjective. It's preferred to use "female".

So, while these may be perfectly fine, they are not adjectival uses of "woman":

The woman pilots the plane.
At Airline X, women pilot all of the planes.
_{*Note that in these examples, "pilot" is a verb, not a noun.}

The preferred use would be:

Female pilots were well known as early as the 1960s.

As a note, none of these uses are "possessives". There's no show of ownership at all. It's just describing the type of pilot you're talking about.

This section options 1 and 4 both use the possessive but 2 and 3 do not:

1. Women's jobs
2. Women jobs
3. Woman jobs
4. Woman's jobs.

So, if your goal is to understand the possessive use, I'll ignore 2 and 3, which I don't think should ever be used, regardless of possession.

Version 1 is plural possessive. If that's what you're looking for, this is your choice. "Women" is plural and the "apostrophe s" makes it possessive.

Version 4 is singular possessive. "Woman" is singular and the "apostrophe s" makes it possessive.

If you look a little more carefully at the question though, we aren't comparing the possessive structure Tom's car and car Tom's. The sentence actually says "that car is Tom's", and the is here makes all the difference.

Another thing about possessives is that we can also use them instead of a noun phrase to avoid repeating words, for example:

Whose coat is this? It’s my wife’s [coat]. > It’s my wife’s.

In your case the sentence states

This car is my car, and that car is Tom's [car].

...and the possessive allows us to remove the word car at the end of the sentence to give us...

that car is Tom's [car] > that car is Tom's.