Hello Joan - good thinking and it will minimuse confusion.
I am not sure exactly what you are after just yet but your information suggests you know little about Thomas and Elizabeth.
Based on that assumption I will offer a couple of things that I have managed to find. This will determine where you are at and we can work from there.
The family is easily found in the 1851 Census at Reawla Lane, Gwinear when only the four youngest children were at home.
From this I determined that Elizabeth was a little older than Thomas and it appears both were born at Gwinear as you mentioned.
A search from 1793-1803 for Thomas Williams gives only one possibility in IGI so that is a starting point and the names of his parents suggest he is the right man.
Thomas son of Colan and Mary Williams bp. 24th June 1798 Gwinear
Elizabeth Uren is a different matter and there are four entries for that same period.
Bearing in mind she was a little older than Thomas then we are probably looking at one of the first two entries although it must be considered that her baptism might have been delayed.
Elizabeth daughter of John and Elizabeth Uren bp. 5th March 1797 Gwinear
Elizabeth daughter of George and Elizabeth Uren bp. 2nd July 1797 Gwinear
Of these two I would favour her being the daughter of John Uren but this is based solely on the list of children you have supplied.
In that list there are four sons -
Thomas would have been named for his father
William -
Colan - certainly named for his grandfather
JOHN - 'possibly' named for Elizabeth's father
There was an Elizabeth Uren daughter of William baptised at St Erth in 1798.
St Erth shares a small border with Gwinear so this might also be a possibility although there appears to be no record to suggest this Elizabeth was not born at St Erth.
It is unfortunate that none of the children were given a second Christian name that might have helped positively identify their mother.
In the 1841 Census there are two additional members of the Williams household.
William Williams age 45
Mary Williams age 84
I would suggest that Mary was certainly the mother of Thomas and that William was probably his brother.
This might also be the source of the name of Thomas Williams' son.
At the moment I favour John and Elizabeth being the parents of Elizabeth Uren but that also adds something to think about.
Using IGI only for the time being I tried a search between 1783 and 1803 to see what marriages there were for a John Uren to someone named Elizabeth.
The result was just one!
John Uren married Elizabeth Jane 26th March 1796 at Illogan
There are no children baptised to this couple at Illogan and Elizabeth was the first child at Gwinear.
Keep an open mind until more substantial information can be found - but I think this is most likely the Elizabeth you are looking fore.
CT