Looking for information on the relationship between these people: Christopher Smyth and Thomas Smyth ; Margaret Hazlett and Eleanor Hazlett

I have a DNA match on ancestry.com  (estimated 2nd-3rd  cousin) named Anne.  We have been texting trying to find our common ancestor,  I believe that we may have 2 common ancestors.  My Grandfather was Robert James Smith who was born in County Tyrone in 1885 and died in Philadelphia Pennsylvania, US in 1969. His Father was Alexander Smyth born Oct 1835 in Co. Derry and died Nov. 1924 in Copney, Carrickmore,Co. Tyrone.  Alexander's father was Christopher Smyth born abt. 1797 and died April 1875 in Co. Tyrone.  I Think his Father may have been named Thomas Smyth.

Ann has a Thomas Smyth on her family tree born 1798 born in Maghera, Londonderry NI and died Sept 14,1868 in Falgortrevy, Londonderry NI.  I am wondering whether Ann's Thomas Smyth might be a brother or cousin to the Christopher Smyth , my second great-grandfather.  If anyone has information on these gentlemen that they can share I would greatly appreciate it.

My 2nd great grandmother was Eleanor Hazlett.  I believe she was also from Co. Tyrone but I do not have confirmation. She would have been born in the early 1800's.  She was married to Thomas Denison, born about 1803 and died about 1871.

Ann has a Margaret Hazlett on her family tree born 1798 and died in 1878. Margaret was married to the above mentioned Thomas Smyth.  I am also interested in finding out if Eleanor and Margaret are related and how they are related.  I appreciate any help on this quest.  Anne and I will be meeting for the first time in person next month.