Hello native English speakers
Sorry to disturb you.

1. at Smith's , the bookseller.
2. at Smith's , the bookseller's.
3. at the Smith's , the bookseller's.
Question: Which is/are grammatically correct?
Do these noun phrases have the same meaning?
Which is the correct meaning of the "at Smith's , the bookseller",
the "at the house of Smith who is a bookseller",
or, the "at the workplace of Smith who is a bookseller"?
By the way, is its meaning related to the context?

Question

Hello native English speakers
Sorry to disturb you.

1.  at Smith's , the bookseller.
2.  at Smith's , the bookseller's.
3.  at the Smith's , the bookseller's.
Question: Which is/are grammatically correct?
Do these noun phrases have the same meaning?
Which is the correct meaning of the "at Smith's , the bookseller",
the "at the house of Smith who is a  bookseller",
or, the "at the workplace of Smith who is a  bookseller"?
By the way, is its meaning related to the context?

Answer

You need to provide context. These are fragments of a sentence that have no meaning on their own.  I could use each of your three fragments correctly in some context.

Answer

To be totally accurate their name is singular, WH Smith, but people here in England do call them Smith’s too.

It therefore should be bookseller, as it’s singular. However, we would use the plural as they have more than one shop. Booksellers because it’s a plural noun, not a possessive noun, so you don’t need the possessive ‘s.

Smith’s the booksellers

Answer

Americans use ‘bookstore’ for a normal business that sells books. I suppose ‘bookseller’ could be used for an individual or a niche business.