Definitions. The government has helpfully pointed out the definitions that they use

"Man": from the Equality Act 2010: 'A male of any age'

"Woman": from the Equality Act 2010: 'A female of any age'

and from the Gender Recognition Act consultation at https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/721725/GRA-Consultation-document.pdf ..

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"Sex": 'Assigned by medical practitioners at birth based on physical characteristics. Sex can be either male or female.'

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"Gender": 'Often expressed in terms of masculinity and femininity, gender refers to socially constructed characteristics, and is often assumed from the sex people are registered as at birth.'

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"Gender identity": 'A person’s internal sense of their own gender. This does not have to be man or woman. It could be, for example, non-binary. '

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"Transgender / Trans": 'Umbrella terms used to describe individuals who have a gender identity that is different to the sex recorded at birth. Non-binary people may
or may not consider themselves to be trans.'