Are there differences between "lady" and "woman" ?
Google say lady is a polite social woman. But we don't use them just as this. Do we? English isn't my native language so I am better clarifying myself.
"Lady" can be used to refer to someone of higher or lower social rank. When it's spelled with a capital letter, it is the title of a woman with the equivalent rank of a Lord, or a woman who is married to a Lord. As "just a word", though, it usually refers to somebody who is of a different social rank from yours. You would use the terms "cleaning lady" and "bag lady" just as much (and probably more in these less-formal times) as you would "lady of the house" and other sorts of "you are more important than me" phrases.
One needs to watch the use of "lady" these days. Because it has been as much a word that comes automatically with marriage as one that may be earned, it is sometimes felt as belittling, dismissive or condescending; something like calling Jane, who is married to John Smith, Mrs. John Smith. The word itself isn't a bad one, and can be used in very positive ways, but many of its uses—uses that once would have been the height of proper manners—are very much unwelcome these days.
An analogy should illustrate the difference well:
Lady : woman :: gentleman : man.
That is, "lady" and "gentleman" typically occur in the same contexts, as do "woman" and "man". Examples:
"Ladies and gentlemen" as a term of address in public speaking.
Women and Men, the title of a novel by Joseph McElroy.
Both user3820386 and Stan Rogers answers are correct, but there is more to the question. There has been a generational shift in the meaning and implications of "lady", at least in the US. For instance, my father (born 1913) used to tell the joke, "What's the difference between a diplomat and a lady?"
If a diplomat say yes he means maybe, if he says maybe he means no, and if he says no he's no diplomat.
If a lady say no she means maybe, if she says maybe she means yes, and if she says yes she's no lady.
In the 1950s, the animated Disney movie "The Lady and the Tramp" http://movies.disney.com/lady-and-the-tramp was a popular family movie, but it included a play on words with the juxtaposition of "lady" and "tramp", with the latter meaning a sexually promiscuous woman.
At the same time, "lady of the evening" was a euphemism for prostitute.
With the advent of the Sexual Revolution, the aspect of compulsory chastity is no longer part of the definition of lady. As far as I know.
A lady was a woman with an higher rank in society. Nowadays lady and woman means the same (but lady is more complimentary than woman).