Terrell Moore was born ca 1812/13 (per 1850 census) in Caswell County, North Carolina (per 1850 census).

I do knot know who Terrell's parents were, for I've done no Moore research in Caswell County. That is outside of my geographic area of interest for Moore research. My prime interest in Terrell is that he later moved to Macon County, NC which is within my area of interest. The given name "Terrell" certainly suggests a connection to the Terrell family, and it is interesting that his wife was a Terrell, so possibly a cousin of his.

Terrell Moore would have been about 7 years old by the time of the 1820 census, so he ought to be enumerated in the "Under 10" age group (born ca 1810/20). The 1820 census index for Caswell County shows several Moores listed. I have not checked them to see who had sons this age.

For the 1830 census, Terrell would have been about 17 years old. He should be enumerated in the 15-19 age group (born ca 1810/15).  The census index shows 13 Moores in Caswell that year. I have not checked them to see who had a son this age.

On 2 Apr 1834, Terrell Moore obtained a marriage bond in Caswell County to marry Ann Terrell. Madison McMury was bondsman. Ann was born ca 1816/17 in Caswell Co, NC (both facts per 1850 census). I don't know who her parents were.

I was unable to locate them on the 1840 census. Based on their children's birth places, they should have been in Caswell County still. A hunch told me he was probably misspelled in the index, a "Ferner Moore" stood out, and after checking it out, I think it does say "Terrell" Moore, but I can clearly see why the indexer had trouble with it. Of special note is his neighbors, Ischella Moore (1790/1800) (possibly his widowed mother?) and Thompson Moore (1810/20), possible brother?.

1840 census analysis (based on available evidence): (Explanation of this census)

1840 Caswell Co, NC pg 131 Terrell Moore 1000100000000-1000100000000
Analysis:
1 Male(s) 20-29        (1810-1820)	Terrell MOORE (1812/13)
1 Male(s) 0-4          (1835-1840)	Andrew MOORE (1836/37) son
1 Female(s) 20-29      (1810-1820)	Ann TERRELL Moore (1816/17) wife
1 Female(s) 0-4        (1835-1840)	Elizabeth MOORE (1838/39) daughter

Some time between ca 1846 and ca 1849, the Terrell Moore family moved west to Macon County, North Carolina. I don't know what drew them there. Other Moore families already lived there, but I know of no connection.

Terrell and family were listed on the 1850 census in Macon County. They were not listed near any other Moore families. 

1850 census abstract: (Explanation of this census)

(Note: The dates at the end of each line are not part of the original census, but are approximate birth years based on age)

1850 MACON CO, NC Page 359   House/Family #  582/ 593  - TENNESSEE VALLEY Twp

MOORE TYRREL          37 M W LABORER                    CASWELL CO, NC       1812/1813
MOORE ANNA            33 F W                            CASWELL CO, NC       1816/1817
MOORE ANDREW          13 M W                            CASWELL CO, NC       1836/1837
MOORE ELIZABETH       11 F W                            CASWELL CO, NC       1838/1839
MOORE JOHN             7 M W                            CASWELL CO, NC       1842/1843
MOORE WILLIAM          4 M W                            CASWELL CO, NC       1845/1846
MOORE LOGAN            0 M W 10/12                      MACON CO, NC         1849/1850

They were gone from Macon by the time of the 1860 census. I don't know where they moved to. I couldn't find him on the 1860 census index, though there are certainly numerous ways to spell his first name.

I don't know where he was in 1870 either, but by 1880, he was back in Caswell County, NC listed in Hightower Township. ** I don't have this entry typed up yet.