What you will be looking at is an extract from the Old Parochial Register for New Monkland parish.
Anyone who lived in the parish, no matter what religion or what church they attended - or of no religion at all, was entitled to be interred in the parochial burial ground. In this case, the churchyard surrounding the parish church at Glenmavis.
As I said in my previous post, the West parish church (by 1841 a Quod Sacra parish) did not have a burial ground and so the parishioners would have to have used the churchyard at Glenmavis.
So, this Mortcloth register belongs to the parish church and the fact that it mentions which Quod Sacra parish the deceased belonged to is a little bonus for you. It also eliminates the possibility of them being interred in the Chapel St, Wellwynd (Burgher) Church or Broomknoll St burial grounds within Airdrie burgh.
There were a few other churches in Airdrie at that time, all Secessionist churches, the Cameronians were in Upper Bridge St and the "Auld Lichts" (a Burgher breakaway congregation) built a church with a surrounding burial ground round about 1804 I think, in Broomknoll Street.
Lastly, St Margaret's Roman Catholic church in Airdrie was founded in 1836, the oldest Catholic church in the Diocese of Motherwell, it doesn't have a burial ground so its parishioners would have been interred at Glenmavis until the opening of St Joseph's R.C. cemetery, about 1855 I think.