Pair like man/woman but clearly for sex not gender [closed]

Standard usage in the English language does not distinguish these concepts. To the vast majority of people, "sex" and "gender" are synonyms, and as such there is no common convention as to whether gendered words refer to gender or sex. Any attempt to distinguish them will require either modifiers or laying out a convention at the start of the text for how terms will be used. Which to use will depend on your target audience, but here are some suggestions:

• Use different sets of common English terms for the two concepts, such as "man" and "woman" for gender and "male" and "female" for sex. If you do this, you must explain that this is the convention you are using at the start, and may want to include reminders later on.
• Use modifiers on gendered words. Something like "biological male" and "identified male". I would recommend against having only one of the terms marked, such as using "biological male" for sex and "male" for gender, to prevent confusion or implication that one is more valid than the other.
• Use other ways of marking gendered words, such as "female (s)" and "female (g)" to distinguish the gender and sex senses of the words. This can harm readability by disrupting the natural flow, but it's fairly compact and avoids any ambiguity.
• Use existing jargon if this is an academic audience. Check the literature of the field for the proper terms, though still take care to avoid ambiguity as your audience may be multidisciplinary.

polar pair of terms that clearly refers to organisms with a specific sex

You don't specify species, so I will broaden this beyond humans. Most polar pairs of terms for non-human species are generally used to discuss biological sex - cock/hen, bull/cow. When co-opted to describe humans, these terms sometimes become transferred to refer to gender roles though.