In India we routinely refer to all women as ladies, not only in Indian English but also using the English loanword 'lady/ladies' in Indian languages.
These seats are reserved for ladies.
The old lady running the roadside lunch house brought him rice and curry.
The new District Collector is a lady.
Calling somebody a 'woman' is usually perceived as rude here, with the notable exceptions of news journalism, law, bureaucratese and scientific literature:
Bangalore woman wins Maths Olympiad.
Fifty women were studied for symptoms of clinical depression related to work pressure and marital stress.
My client is a woman who has suffered extreme mental torture from her husband and in-laws, and I submit this is another strong reason for demanding a substantial compensatory divorce settlement.
Rule 3a: Employees shall not avail more than 3 days paid sick leave per month. THIS RULE APPLIES to both men and women.
However the word 'woman' may be seen used admiringly of somebody (and especially in social media) in statements such as
'Mrs. Sharma was a great woman'
'(my mother is) a woman of substance, a woman full of grace'
'You are one determined woman!'
Also, many modern women frankly refer to themselves as women, as in
"I am a simple, fun-loving and practical woman." (somebody's self-introduction, as for a profile page on ELU.)
I think this is the influence of modern British/ American English, but 'woman' and 'lady' have always been fundamentally interchangeable as used in India, with 'lady' being by far the accepted polite usage. However I came to know that, unlike in Indian English, these 2 words used to be distinctly different expressions in Britain and the USA, both in formal and colloquial use.
So how do native English speakers in Britain/ America/ the World use lady/woman nowadays? What connotations does each word carry? Are the words distinct or interchangeable in contemporary usage?