What is the difference between “Gay” and “Homosexual"? Is it only by gender?

I was interested in the line “...most Americans use the word 'gay' now instead of 'homosexual'” in Maureen Dowd’s article titled “Happily Never After?” in today’s (April 2) New York Times:

I’m worried about how the justices can properly debate same-sex
marriage when some don’t even seem to realize that most Americans
use the word "gay" now instead of "homosexual"; when Chief Justice
John Roberts thinks gays are merely concerned with marriage as a
desirable "label," and when Justice Samuel Alito compares gay marriage
to cellphones.

When you say “instead of,” it gives me an impression that they are different things, for examples, “I use margarine instead of butter,” “They use acrylic panels instead of plate glass for windows” and "The new car uses aluminum instead of steel plate for the body."

However, when I checked Oxford English Dictionary, it renders “gay” as:

a.1 (of a person, especially a man) homosexual.

1. relating to or used by homosexuals:

n. a homosexual, especially a man.

Also OALD defines Gay as:

a. (of people, especially men) sexually attracted to people of the
same sex. [Syn.] HOMOSEXUAL

Aren’t “gay” and “homosexual” the same thing except “gay” being applied to men?
What’s the difference between “gay” and “homosexual” other than gender attributes?

Answer

Both gay and homosexual can be used for both sexes, and they mean mostly the same thing; the differences are subtle.

Probably because the word lesbian exists as well, one is slightly more likely to refer to men when using the word gay; but note that it is very often also used for women. When used as a noun, gay seems to refer to men a bit more often than as an adjective, although it is still very often used to refer to both men and women. It rather depends on context. The word homosexual seems to be completely gender-neutral.

Gay is more informal: homosexual is more formal, and so it is more likely to be used in e.g. medicine and biology. As a consequence, using homosexual can sometimes sound a little bit as if you were describing patients, as if it were some mental illness. This effect is not very strong or ubiquitous, but it is sometimes there. It is stronger when used as a noun (an homosexual, homosexuals). Note that gay is currently in the process of being used more in formal contexts too.

The word homosexual is older. Because homosexuality was long treated as a disease or at least as undesirable, some of this old negativity still clings to the word homosexual, especially as a noun. It is as if you were referring to the past, although this effect, too, is not that strong.

I think this is also the reason why the word gay came to be used (around the 1960s? earlier?) to refer to homosexuals: they wanted a more positive-sounding word. You will find that most gays will mainly use gay, except in a scientific context; and even there, homosexual as a noun has become almost impossible. If you were to say homosexuals, and you weren't over 50 or a bit reactionary in general, I would think you were joking.