Part of me thinks it is hard to imagine that there were two Jane Embletons of that age, but part of me wonders why Jane would be a negro (ie. full blooded African) slave having been a 'free mulatto'.
It depends to some extent on what year/s are under consideration. Full emancipation was not until about 1835, and some slave owners held on to their slaves even after that. Many slave owners freed their slaves as legislated, but then tied them to contracts or "apprenticeships" of one kind or another for a number of years in order to continue to have a cheap workforce for their estates or businesses.
But I have seen Manumissions (voluntary freedom given slaves) being implemented as far back as the 1780s and 90s. It could be expensive in the Colonies, but was cheaper done in England, and there were some slave owners who either sent the slaves being manumitted to England for the purpose, or had family members or their commission agents perform the function for them in England.
Reasons for manumitting were many, including slave women being the owner's partner (or at least one of several), his/her children, or of some great service along the way. Some slaves were freed through their master's/mistress' Will upon (the owner's) death.
Many people today see black and white as, well, black and white. But there was considerable racial intermingling. One native Governor General is known to have remarked that - in Barbados, at least - there were very few long-time Barbados families of either colour who did not have some of the other colour in them somewhere.
Also bear in mind that the official "description" (negro, mulatto, etc.) was not a guarantee of their real actual "colour". The record keepers of the day had very little supervision and could "describe" people any way they wished (until Emancipation, when the practice ceased), and any person could be so "described" so long as they were not white and English. For instance, an olive-skinned (free) Portugese or Italian resident could be "described" in whatever record as a mulatto - and, since few people could read, nobody would be the wiser for many years afterwards, by which time it was too late to change the record.