Sex means the same, but When people talk about Gender, I think it is taken to mean (quite incorrectly) their physical sex as well as their sexual identity.
probably because there are 2 types of Sex, Male/Female. and until recently 2 types of Gender Male/Female.

If you asked a Gender neutral person what their Sex was, What would their response be?

"It was a Team effort, I guess it took all players working together to lose this one"

Does it matter?

They will have a biological sex and most of the time I'm going to get that right just from looking at them.

If someone wants to view themselves a certain way that's cool.
If I want to view them a certain way that's cool as well.

'Who are you and how did you get in here? I'm a locksmith. And, I'm a locksmith.' (Leslie Nielsen)

You are probably correct with this, "we have lost the distinction".

I always thought that 'sex' was the biological difference, male and female, and 'gender' was the characteristic difference, masculine and feminine (and also neuter/common/indifferent). Masculine female = tomboy, feminine male = pansy etc.

Systematically dragged down by the lawmakers

Harry Miller: Legal victory after alleged 'transphobic tweets'

There is another infection which is doing the rounds its called common sense and it appears to be affecting judges, thank god.

[Link]

I have a problem with the police recording non crimes and so apparently does the Court of Appeal although they don't go as far as I would like.

One more point

Condemned by people who run around a field with a stick clenched between their thighs.

Gender, noun

The male or female sex, or the state of being either male or female:

[Link]

"You can lead a horse to water but a pencil must be lead"

Stan Laurel