There are the physical features and/or reproductive organs one has which is not always binary (true hermaphrodites, psuedo-hermaphrodites and other variations of nature for example).

Then there is the psychological identity or sexual identification one has.
Gender could be taken to be a psychological state whereas sex could be taken to be the physical features but I don't think these terms are understood or used exclusively in that sense. The whole issue has become somewhat complicated of late.

I updated my OP, anything you would like to add?

Well many are rejecting the traditional binary sexual or gender identity categories. On facebook one has the following options.
The following are the 58 gender options identified by ABC News:

Agender
Androgyne
Androgynous
Bigender
Cis
Cisgender
Cis Female
Cis Male
Cis Man
Cis Woman
Cisgender Female
Cisgender Male
Cisgender Man
Cisgender Woman
Female to Male
FTM
Gender Fluid
Gender Nonconforming
Gender Questioning
Gender Variant
Genderqueer
Intersex
Male to Female
MTF
Neither
Neutrois
Non-binary
Other
Pangender
Trans
Trans*
Trans Female
Trans* Female
Trans Male
Trans* Male
Trans Man
Trans* Man
Trans Person
Trans* Person
Trans Woman
Trans* Woman
Transfeminine
Transgender
Transgender Female
Transgender Male
Transgender Man
Transgender Person
Transgender Woman
Transmasculine
Transsexual
Transsexual Female
Transsexual Male
Transsexual Man
Transsexual Person
Transsexual Woman
Two-Spirit

Loosely, sex refers to the person's biological sex organs and gender refers to how the person sexually identifies themselves.

Gender could be taken to be a psychological state whereas sex could be taken to be the physical features but I don't think these terms are understood or used exclusively in that sense.

Gender isn't a psychological "state.' it's an identity of each person they have 24/7 unless it changes. That's like saying being Gay or Straight are psychological states. They're not.

Gender isn't a psychological "state.' it's an identity of each person they have 24/7 unless it changes. — John Harris

But let's say, "I'm straight" that's not something that's gonna change, I'm either straight or I'm not. So I don't understand why it would change. Is it based on the weather? "it's sunny today, so I like men", "it's rainy today, I like pots" I feel as though people, like my acquaintance in the OP, who openly state that gender is fluid, is like saying that weather doesn't have its purposes. I believe Weather, much like our gender, are set so that you know what to call rain, or wind, or storm, just as you call male or female or "both".

People's sexual identity can vary over time, so I think gender not only is not binary but it also represents a psychological state, you are free to disagree.

58 gender options identified by ABC News — prothero

Thank you for that, made me chuckle

But let's say, "I'm straight" that's not something that's gonna change, I'm either straight or I'm not

Of course it can change. Many Gay people thought they were Straight for a long time and even married and had children before they realized they were Gay and became actively Gay.

People's sexual identity can vary over time, so I think gender not only is not binary but it also represents a psychological state, you are free to disagree. — prothero

It's not so much that I disagree, it's just more of I don't fully understand

Of course it can change. Many Gay people thought they were Straight for a long time and even married and had children before they realized they were Gay and became actively Gay. — John Harris

I just meant for me personally

People's sexual identity can vary over time, so I think gender not only is not binary but it also represents a psychological state, you are free to disagree.

Then you must think your being Straight or Gay is a psychological state, since that could change over time, too. So, you are misusing the term "psychological state."

We can have sex with any gender but we can't have gender with any sex.

John Harris I just meant for me personally
Of course it can change. Many Gay people thought they were Straight for a long time and even married and had children before they realized they were Gay and became actively Gay.
— John Harris

But we weren't just talking about you personally, so you were wrong to correct me.

But let's say, "I'm straight" that's not something that's gonna change, I'm either straight or I'm not. — Anonymys

I was making an example of myself, I wasn't making a metaphorical person up, I was literally saying that I'm straight, and that is not going to change

*thumbs up*

Gender isn't a psychological "state.' it's an identity of each person they have 24/7 unless it changes.
— John Harris

But let's say, "I'm straight" that's not something that's gonna change, I'm either straight or I'm not. So I don't understand why it would change. Is it based on the weather?

Don't lie. Above you are clearly criticizing my claim that if gender is a psychological state, being Gay and Straight are, too....and not just you. Because I certainly wasn't just talking about you.

No, really, I was using myself as an example for the purpose of the question

Then you must think your being Straight or Gay is a psychological state, since that could change over time, too. So, you are misusing the term "psychological state." — John Harris

I am afraid you need to expound or elaborate on that. People often change their mind (psychological state) over time, especially younger people, about their gender identification, many do not.

Go away. I don't talk to people who don't debate/discuss in good faith.

I don't have to expound or elaborate on anything. Do you think being Gay or Straight is a psychological state?

I don't usually talk to argumentative......... but here we are. Don't let your pride get in the way of what you really see, you and I both know that I clearly used myself as an example

And I was talking about all people, not just you, and that was what you addressed. Don't let your pride and obtuseness keep you from seeing that.

And that's the last post of yours I read, Mr. Argumentative.

You spelled my tag wrong

It is not that simple. I don't wish to give the impression it is solely a matter of choice, and I don't refer to "psychological state" to mean it is necessarily a conscious decision or a decision that does not have neurological correlates. I merely mean to point out that one's physical characteristics are not always concordant with one;s gender identification and that a binary model is inadequate for human behavior..

The only one is making it difficult is you. Do you or do you not think being Gay or being Straight is a psychological State. A simple yes or no question. If you can't answer that, what you said about gender being a "psychological state" becomes inevitably wrong.

This is not a courtroom, it is a philosophy forum and these types of questions do not lend themselves to a simple yes or no question. I think sexual preferences or or sexual fetishes have a strong subconscious component (i.e. are not conscious choices), and there is some evidence of differences in the structure of the brain. So gender identity (much less sexual behavior) is both psychological and physical and not necessarily fixed in the manner you imply. It seems you feel you are here to win arguments and not necessarily to try to understand other points of view. The range of variation in physical sexual features is complicated enough much less peoples gender identification. Is gender identification, in your view, mental or physical, or both?

Sorry, then if Gay and Straight aren't psychological states, then there's no way gender can be, since all of those can change.

And stop with the ad hominem attacks; they're very childish.

Many people think their sexual orientation is natural -- it's a given of nature, whether they are gay or straight. You say (correctly) that some presumably straight people discover that they are actually gay. I don't believe any of the many gay men I know have discovered they were actually straight. (I'm not considering bisexuality here, at the moment.)