It looks very likely that they are one and the same. I think you'd be safe enough making that assumption.
There's a record of the marriage of John Spence and Jane Jack in 1830 in the parish of Bolton. That's Bolton in the county of East Lothian, not any of the Boltons in England. It is very unlikely to contain any information about their parents.
In 1841 John Spence, 30, born East Lothian; Jane Spence, 35; Charles Spence, 8; and John Spence, 6 are in Morham, East Lothian.
The 1851 census lists in Haddington John Spence, 45, jobbing gardener, born East Lothian; wife Jane, 54, born Crieff, Perthshire and son John, 16, born Crieff, Perthshire
In the 1861 census John Spence, 49, jobbing gardener, born Haddington, and his wife Jane, 60, born Crieff, are in Haddington.
There's a death of Jane Spence or Jack in Haddington in 1864, and a death of a John Spence in the same year and place who may be her husband.
To see any or all of the originals of these documents, go to
www.scotlandspeople.gov.uk, buy a few credits, and use them to view the images of the documents. They cost 6 credits (GBP 1.50) per image.
The death certificates ought to tell you the full names of the couple's parents including their mothers' maiden surnames, but the latter aren't in the index so they may be missing from the documents.
