well, Morgan isn't an uncommon name, so no reason they would be related. How far back have you traced the 2 Morgan families?
Working backwards
1871 New Mill Village, Miskin RG10/5380 folio 6 pg 5
Daniel Morgan head mar 42 carpenter b. Pendoylan
Catherine wife 35 b. St Mary Church
William son 9 b. Llantrisant
Thomas son 7 b. Llantrisant
Ebenezer son 5 b. Llantrisant
Lewis son 4 b. Llantrisant
Ann Thomas 19 general servant b. Dowlais
marriage reg
Daniel Morgan june qtr 1861 Bridgend vol 11a pg 565 with Catherine Mathews on the same page
1861 Tyn y Cae, Pendoylan RG9/4042 folio 20 pg 5
Daniel Morgan head mar 63 wheelwright carpenter b. St Andrews
Jane wife 55 b. Pentyrch
Daniel son 32 wheelwright carpenter b. Pendoylan
David son 29 wheelwright carpenter b. Pendoylan
Ebenezer son 25 wheelwright carpenter b. Pendoylan
Margaret dau 15 b. Welsh St Donats
the only census with a likely Sarah & Catherine together is 1841, and it doesn't give relationships
1841 Llanharan Village HO107/1416/10 folio 7 pg 9
William Mathew 50 butcher
Mary 41
Margaret 20
Mary 15
Sarah 8
Catherine 5
Evan 3
Thomas 3 months
/
Margaret Jenkin 79 independent
marriage reg
John Morgan sept qtr 1858 Cardiff vol 11a pg 333 with Sarah Mathews on the same page
1861 Llantrithyd RG9/4041 folio 131 pg 3
John Morgan head mar 30 farmer of 14 acres employing 1 man b. Llantrithyd
Sarah wife 27 b. St Mary Hill
Mary dau 1 b. Welsh St Donats
Alice dau 1 month b. Llantrithyd
Ann Morgan visitor 37 house servant b. Llantrithyd
Mary Traherne 18 general servant b. Llangrallo (?)
John isn't with parents in 1851, but I think this is his fmaily in 1841. Do you have marriage certificate to confirm father's name?
1841 Llantrithyd HO107/1417/16 folio 7 pg 8
Chrisr (Christopher) Morgan 75 farmer
Margt 50
Thos 26 labourer
Rich 19
Eliz 23
Ann 23
Chrisr 15
John 10
John Mumford 9
all born in county
Margaret's burial
http://www.freereg.org.uk/cgi/SearchResults.pl?RecordType=Burials&RecordID=6925270& Christopher's
http://www.freereg.org.uk/cgi/SearchResults.pl?RecordType=Burials&RecordID=6925383If you have the 2 marriage certs, could you confirm or not, the Morgan families, before we try to go further back.