See James Smith of Newtown, Long Island and his Descendants in Huntington, and his Brother John Smith of Hempstead,  by Frederick C Hart, Jr.  in The New York Genealogical and Biographical Record Vol.134, No. 3, page 163-174, 294-298

Several loosely defined groups of settlers and religious reformers migrated from Watertown, Massachusetts in 1635, to Springfield, Massachusetts, or to Wetherfield, Connecticut; in 1641 to Stamford Connecticut; and in 1644 to Hempstead, Long Island, then under Dutch control.  Many in this group were followers of Rev. Richard Denton

Among these were Richard Gildersleeve, Jeremiah Wood, Jonas Wood Sr, Jonas Wood, Jr. Edmund Wood, James Pyne (Pine), John Strickland, John Smith Sr, John Smith Jr, later known as John Rock Smith.

There is no record to support the idea that John Smith, Sr, and John Smith, Jr, were father and son, merely older and younger. And there is nothing specific to identify John Smith, Jr, as John Rock Smith, although John Rock Smith of Hempstead deposed in 1675, at age 60, that he remembered the marking of the line between Stamford and Greenwich in 1641.  And Frederick Hart makes the case in his article, cited above, that the widow of John Smith, Sr, was most probably the second wife of Richard Gildersleeve, whom John Nan Smith referred to as his step-father.

John(?) Smith of Stamford, whose widow married Richard Gildersleeve, apparently had three children:
1. James Smith was probably born in or just before 1621, since he was old enough to rent land and
. . .livestock near what is now Long Island City in 1642.  He lived in Hempstead from about 1644 to
. . 1652, when he helped found Newtown, and contributed to the purchase of Indian Land Rights in
. . 1656.  His widow Martha married before March 1661/2 Richard Owen (d.1694).
. 11. James Smith (c.1650)
. 12. Jeremiah Smith (c1652)
2. Elizabeth Smith (c.1622) married c.1641 Jeremiah Wood, Sr. (bp.Jan 1619/20 Halifax, England)
3. John Smith of Hempstead, (1625?-1694) known as John Nan  or Little John, implying that "Nan" 
. . came from an old English word for "small" which derived from the same Latin root as "nano," 
. . meaning small. Some people claim that "Nan" came from "Nantucket" where this John Smith may 
. . have been born. One of the first 20 purchasers of land on Nantucket was a John Smith, and that 
. . was in 1671.(a)  But on 3 June 1659, "Anna the wife of John Smith nants of Hemsteede" testified 
. . concerning a deed signed "at ye house of her father Mr. Richard Gildersleve."(b)  So clearly, the 
. . nickname "Nan" precedes the settlement of Nantucket.
. . (a) The Andros Papers 1674-1676, Christoph, 1989, p.25
. . (b) The Records of the Towns of North and South Hempstead, Long Island, NY, v.1 p.111, citing volume A page161

John "Nan" Smith (1625?-1694) married about 1646 Anna Gildersleeve (1629-before 1671)  And John Nan Smith remained a close neighbor of Anna's father Richard Gildersleeve, who apparently married John's widowed mother.  John married secondly, 1672,  Elizabeth Wickes, daughter of John and Mary Wickes of Warwick, Rhode Island, and widow of Richard Townsend. John's will made 2 July 1694, proved 6 Sep 1694, called himself the "son-in-law" of Richard Gildersleeve and used the same term to identify Richard Townsend, Jr, the son of his second wife.  This leads us to believe the term "son-in-law" would be in modern terms "step-son," giving further evidence that his widowed mother had married Richard Gildersleeve.
. 1. Jonathan Smith (c1647) married Hannah
... . children Thomas, Mary, Ruth, Hannah, and Jonathan "Black" Smith of Merrick
. 2. Hannah Smith (c1650) m(1) c1670 John Smith "Rock" Jr (3 Jan 1651/2-12 Mar 1683/4)  
. ... She m(2) c1686 John Marvin.  see below
. 3. Miriam Smith (c1652) m(1)c1669 John Williams;  m(2) c1682 Elias Durland (1656-1780)
... . children John, Miriam, Samuel, Richard, Thomas and Ann Williams; and Elias and John Durland
. 4. Jeremiah Smith (1656-1726) m.c1679 Hannah Carman, m(2) Hannah, m(3) Anna Cornell
. ... children Jeremiah, Hannah, Elizabeth, Ruth, John, Ann, Richard, Thomas, and James Smith
. 5. Mary? Smith  (1666?) married c1686 Samuel Denton Jr (1665-1719) He m(2) before 1697 Abigail
... . Barlow, widow of Jonathan Rowland. His children: Samuel (b.14 Oct 1687) Ruth, John, Martha,
... . Mary, John (again), Deborah, twin daughters not named died in infancy, Joseph, Geziah, Jemima,
... . and Anna.  Other than Samuel, we are uncertain of birth order and which mother.
. 6. Elizabeth Smith (alive and single in 1698) Possibly the daughter of John's second wife.
. S. Richard Townsend Jr (c1671-c1737) married before 1706 Ruth Marvin (20 Dec 1687) see below

Hannah Smith (c.1652) married about 1670 John Smith "Rock" Jr (3 Jan 1651/2  - 12 Mar 1683/4)  She married secondly about 1686 John Marvin (1649-1708) son of Robert Marvin. 
The August 31 1698 census of Hempstead lists Roberd, John and Hannah Marvill with children Ruth, Hannah, Jereme and Robert Marvill Jr, and Richard, Timothi and Mary Smith.
. 1. Sarah Smith (c.1670) married about 1690 William Pine (c1666-1737) of Hempstead
. 2. Timothy Smith
. 3. Richard Smith (d.1711) married Cathie Smith, daughter of Philip Smith and Margariet Blanck
. 4. Mary Smith
. 5. Ruth Marvin (20 Dec 1687) married before 1706 Richard Townsend Jr (c1671-c1737)
. 6. Hannah Marvin (1689) married a Whitman
. 7. Jemima (Jereme?) Marvin
. 8. Robert Marvin (d.1775) married Phebe
.

Margaret Edwards (1789-1864) m.1821 Thomas Tate (1775-1838)

Thomas Edwards Tate (1821-1914) m.1845 Mary Vernon Cutrer (1825-1892)

Frances Mary Tate (1852-1881) m.1871 Walter Edwin Tynes (1848-1928)

Jeanne Marie Tynes (1878-1958) m.1913 Carson B Matthews (1874-1948)

Frances Mary Tate Matthews (1917) m.1949 Virgil Raymond Liptrap (1907-1977)

James Matthews Liptrap (1951)